Question

if cos^2theta - sin^2theta =tan^2theta, then prove: cos theta =1/√2 cos theta​

Answer 1

Answer:Given (cos

2

θ−sin

2

θ)=tan

2

ϕ

To prove:

cosϕ=

2

​

cosθ

1

​

(cos

2

θ−sin

2

θ)=tan

2

ϕ

add 1 on both sides

(cos

2

θ−sin

2

θ)=tan

2

ϕ+1

cos

2

+(1−sinθ)=(1+tan

2

ϕ)

cos

1

θ+cos

2

θ=sec

2

ϕ

⇒ 2cos

2

θ=sec

2

ϕ

⇒ 2cos

2

θcos

2

ϕ=1

⇒ cos

2

ϕ=

2cos

1

θ

1

​

⇒ cosθ=

2

​

cosθ