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Chapter 6: Trigonometric Identities Exercise – 6.2

Question: 1

If cos θ = 4/5, find all other trigonometric ratios of angle θ. 

Solution: 

We have: sin θ = 1 - cos2θ

= 3/5

Therefore, sin θ = 3/5

 

Question: 2

If sin θ = 1/√2, find all other trigonometric ratios of angle θ.

Solution: 

We have,

=1/1

=1

 

Question: 3

Solution: 

We know that

 Substituting it in equation (1) we get

 

Question: 4

Solution: 

We know that

sec θ = 5/4

= 1/(5/4)

= 4/5

= cos θ

Therefore, We get

 

Question: 5

Solution: 

= 12/13

 i. e. We get

= 25/1

= 25.

 

Question: 6

Solution: 

= cos θ = sin θ × cot θ

= 1/2

Therefore, on substituting we get

= 3/5.

 

Question: 7

Solution: 

We know that

= 1.

= 1/1

= 1

On substituting we get:

= 4/2

= 2 

 

Question: 8

Solution: 

= 2

cos θ = cot θ. sin θ

On substituting we get:

= 21/8

 

Question: 9

Solution:

On substituting we get

= 40/4

= 10

 

Question: 10

If √3 tan θ = sin θ, find the value of sin2θ - cos2θ.

Solution: 

= sin2θ - cos2θ

= 1/3

 

Question: 11

Solution: 

= 12/13

= 9/3

= 3

 

Question: 12

If sin θ + cos θ =√2 cos(90°- θ), find cot θ.

Solution: 

= sin θ + cos θ = √2 sin θ [cos (90 - θ) = sin θ]

⇒ cos θ = √2 sin θ – sin θ

⇒ cos θ = sin θ (√2 - 1)

Divide both sides with sin θ we get

= √2 - 1.

 

Question: 13

If 2 sin2 θ − cos2θ = 2, then find the value of θ. 

Solution: 

2 sin2 θ − cos2 θ = 2 

⇒ 2 sin2 θ − (1 − sin2 θ) = 2 

⇒ 2 sin2 θ − 1 + sin2 θ = 2

⇒ 3 sin2 θ = 3 

⇒ sin2 θ = 1 

⇒ sin θ = 1 

⇒ sin θ =  sin 90° 

⇒ θ = 90°

 

Question: 14

If √3 tan θ – 1 = 0, find the value of sin2 θ - cos2 θ. 

Solution: 

√3 tan θ = tan 30° θ = 30°

Now, sin2θ - cos2 θ = sin2 (30°) - cos2 (30°)

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