If Sin θ = 5
3 the value of (1 − Cos2 θ) is
A. 9/5
B. 6/10
C. 9/25
D. 25/9
Answers
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1
Given : Sin θ = 3/5
To Find : value of 1 - Cos²θ or 1 - Cos2θ
A)9/5 B)6/10 C)9/25 D)25/9
Solution:
Sin² θ + Cos²θ = 1
=> Sin² θ = 1 - Cos²θ
Sin θ = 3/5
=> (3/5)² = 1 - Cos²θ
=> 9/25 = 1 - Cos²θ
Hence value of 1 - Cos²θ is 9/25
1 - Cos2θ
Cos2θ = Cos²θ - Sin² θ
= 1 - ( Cos²θ - Sin² θ)
= ( 1 - Cos²θ ) + Sin² θ
= 2 Sin² θ
= 2 ( 9/25)
= 18/25
but 18/25 is not in options
Hence correct Question is value of 1 - Cos²θ = 9/25
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