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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°) 