Question

If cos theta = 2 root 2/3 , verify that.
tan^2 theta - sin²theta = tan²theta. Sin ²theta ​

Answer 1

Answer:

Using the identities:

1+tan2θ=sec2θ

1secθ=cosθ

tanθ=sinθcosθ

sin2θ=1−cos2θ

2cos2θ−1=cos2θ

Start:

1−tan2θ1+tan2θ=

1−tan2θsec2θ=

Split the numerator:

1sec2θ−tan2θsec2θ=

cos2θ−sin2θcos2θ⋅cos2θ=

cos2θ−(1−cos2θ)=

2cos2θ−1=

cos2θ