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**Trigonometric**

Formulas are the basics of solving trigonometry questions in the traditional

way. Read on for a thorough understanding of trigonometry questions for SSC

Exams.

Formulas are the basics of solving trigonometry questions in the traditional

way. Read on for a thorough understanding of trigonometry questions for SSC

Exams.

Trigonometry Problems can

be solved by the use of trigonometric formulas, however sometimes this

conventional method can be time taking. In our series on Trigonometry we

started with discussing- the basics of what is trigonometry, the important

formulas and identities and have now come to the 3rd blog. In the 3rd

blog of the series we’ll discuss some traditional and smart methods to solve

trigonometry questions in SSC Exams.

be solved by the use of trigonometric formulas, however sometimes this

conventional method can be time taking. In our series on Trigonometry we

started with discussing- the basics of what is trigonometry, the important

formulas and identities and have now come to the 3rd blog. In the 3rd

blog of the series we’ll discuss some traditional and smart methods to solve

trigonometry questions in SSC Exams.

Before we move ahead, it

would be a good idea to quickly revise the important trigonometric formulas and

identities.

would be a good idea to quickly revise the important trigonometric formulas and

identities.

###
**Set**

1: Questions Based on Trigonometric Ratios and Identities

1: Questions Based on Trigonometric Ratios and Identities

A set of Trigonometry

Problems can be solved by using trigonometric ratios and identities.

Problems can be solved by using trigonometric ratios and identities.

**Problem**

1:sin2

1:

250 + sin2 650 =?

a) √3/2 b) 1 c) 0

d) 2/√3

d) 2/√3

**Solution**

1:

1:

We

know the value of sin only for some specific angles like 300, 450,

600 and so on, so there is no point in trying to substitute the

value. Instead we need to some trigonometric formulas or identities to solve

such trigonometry questions.

know the value of sin only for some specific angles like 300, 450,

600 and so on, so there is no point in trying to substitute the

value. Instead we need to some trigonometric formulas or identities to solve

such trigonometry questions.

sin2

250 + sin2 650 = ?

250 + sin2 650 = ?

=>

sin2 250 + sin2 (900 – 250)

sin2 250 + sin2 (900 – 250)

We

know that for the trigonometric ratio changes for-

know that for the trigonometric ratio changes for-

=>

sin2 250 + cos2 250

sin2 250 + cos2 250

Using

the above identity we get-

the above identity we get-

=>

1

1

Another

way to solve this question is by converting sin2 250 to

cos2 650, in this case also the approach will be similar.

way to solve this question is by converting sin2 250 to

cos2 650, in this case also the approach will be similar.

Therefore

the value of the above trigonometric expression is- Option b

the value of the above trigonometric expression is- Option b

**Problem**

2:cos4θ + sin4θ =2/5, then of 1- 2sin2θ =?

2:

**Solution**

2:

2:

Observing

LHS of the equation below-

LHS of the equation below-

cos4θ + sin4θ =2/5

We

find that it is in the form of-

find that it is in the form of-

Expressing

LHS of the above trigonometric equation in this form we get-

LHS of the above trigonometric equation in this form we get-

(cos2θ + sin2θ) (cos2θ – sin2θ)= 2/5

Using the following trigonometric

identity in the equation we get-

identity in the equation we get-

1

(cos2θ – sin2θ)= 2/5

(cos2θ – sin2θ)= 2/5

Once again using the trigonometric

identity => cos2θ + sin2θ = 1,

in a different form-

identity => cos2θ + sin2θ = 1,

in a different form-

Replacing that value we get-

=>

1- sin2θ – sin2θ = 2/5

1- sin2θ – sin2θ = 2/5

=>

1- 2sin2θ – sin2θ = 2/5

1- 2sin2θ – sin2θ = 2/5

The expression on the LHS is the same

as the expression whose value we have to find.

as the expression whose value we have to find.

Therefore the answer is- 2/5

###
**Set 2:**

Questions Based on Change in Trigonometric Ratios and Angles

Questions Based on Change in Trigonometric Ratios and Angles

A set of Trigonometry

Problems can be solved by using trigonometric formulas where ratios change

based on the value of angles.

Problems can be solved by using trigonometric formulas where ratios change

based on the value of angles.

**Problem**

1:If

1:

sin(600- θ) = cos(𝜶 – 300),

then tan(𝜶 – θ)= ?

(𝜶 and θ

are positive acute angles, where 𝜶> 600 and θ < 600

are positive acute angles, where 𝜶> 600 and θ < 600

a) 1/√3 b) 0

c) √3 d) 1

c) √3 d) 1

**Solution**

1:

1:

Taking

LHS of the given equation and using one of the trigonometric formulas for the

same we get-

LHS of the given equation and using one of the trigonometric formulas for the

same we get-

=>

sin(600- θ)= sin[900- (𝜶

–

300)]

sin(600- θ)= sin[900- (𝜶

–

300)]

Since

the trigonometric ratio on both the ends is the same, we can equate the angles-

the trigonometric ratio on both the ends is the same, we can equate the angles-

600 –

θ= 900- 𝜶

+

300

θ= 900- 𝜶

+

300

𝜶 – θ = 600

As

we per the question, we need the value of-

we per the question, we need the value of-

tan

(𝜶 – θ), so substituting the value we get-

(𝜶 – θ), so substituting the value we get-

tan 600= ?

tan 600=√3

Therefore the answer is-

Option c

Option c

Therefore such questions can

be solved by using the appropriate trigonometric formulas.

be solved by using the appropriate trigonometric formulas.

###
**Set 3:**

Questions Based on converting one set of Trigonometric Ratios in another set of

Trigonometric Ratios

Questions Based on converting one set of Trigonometric Ratios in another set of

Trigonometric Ratios

A set of Trigonometry

Problems can be solved by using trigonometric formulas and identities.

Problems can be solved by using trigonometric formulas and identities.

**Problem**

1:(tan

1:

570 + cot 370)/(tan 330 + cot 530)

= ?

a) tan 330cot 530

b) tan 530cot 330 c) tan 330cot 570 d) tan 570cot 370

b) tan 530cot 330 c) tan 330cot 570 d) tan 570cot 370

**Solution**

1:

1:

Let’s

try and convert these trigonometric ratios into something else and use

trigonometric formulas to finally reduce them to one of the answer options.

try and convert these trigonometric ratios into something else and use

trigonometric formulas to finally reduce them to one of the answer options.

We

know-

know-

=>

tan 570 = cot 330 (i)

tan 570 = cot 330 (i)

=>

cot 370 = tan 530 (ii)

cot 370 = tan 530 (ii)

And

we convert ratios in the denominator to their reciprocal ratios, doing this and

using (i) and (ii) we get-

we convert ratios in the denominator to their reciprocal ratios, doing this and

using (i) and (ii) we get-

=>

cot 330 + tan 530 / [(1/cot 330)

+ (1/tan530)

cot 330 + tan 530 / [(1/cot 330)

+ (1/tan530)

The

idea behind doing this was to get similar ratios and angle values in both the

numerator and the denominator. Simplifying this we get-

idea behind doing this was to get similar ratios and angle values in both the

numerator and the denominator. Simplifying this we get-

=>

cot 330 + tan 530 / [(cot 330 +

tan 530) cot 330 tan530]

cot 330 + tan 530 / [(cot 330 +

tan 530) cot 330 tan530]

=>

cot 330 tan530

cot 330 tan530

Therefore

the answer is- Option b

the answer is- Option b

###

**Practice**

Questions Based on Trigonometric Formulas

Questions Based on Trigonometric Formulas

Question 1: If x = cosec 𝜃 – sin 𝜃

and y = sec 𝜃 – cos𝜃

then the value of x2y2 (x2y2 + 3)

is?

and y = sec 𝜃 – cos𝜃

then the value of x2y2 (x2y2 + 3)

is?

a) 0 b) 1 c) 2 d) 3

Question 2: If sin 𝜃 + sin2𝜃

= 1, then the value of = cos12𝜃

+ 3 cos10𝜃 + 3cos8𝜃 + cos6𝜃 – 1 is?

= 1, then the value of = cos12𝜃

+ 3 cos10𝜃 + 3cos8𝜃 + cos6𝜃 – 1 is?

a) 0 b) 1 c) -1 d) 2

Don’t forget to write your answers in

the comment section and do tell us how this series on trigonometry helped you

understand the topic!

the comment section and do tell us how this series on trigonometry helped you

understand the topic!

Remember to keep practicing!

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