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°)
