Question

tan thita upon 1+ tan square thita =sin thita ×cos thita

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Answer 1

Step-by-step explanation:

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