Evaluate 1-cos 2 theta - 1/1+tan 2 theta .
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It should be 1 - cos²θ +[1/(1+tan²θ)]
or1 + cos²θ - [1/(1+tan²θ)]
Taking 1 - cos²θ + [1/(1+tan²θ)]
∵1+tan²θ = sec²θ
∴1 - cos²θ + [1/(1+tan²θ)]
=1 - cos²θ +[1/(sec²θ)]
=1 - cos²θ +cos²θ
= 1
or1 + cos²θ - [1/(1+tan²θ)]
Taking 1 - cos²θ + [1/(1+tan²θ)]
∵1+tan²θ = sec²θ
∴1 - cos²θ + [1/(1+tan²θ)]
=1 - cos²θ +[1/(sec²θ)]
=1 - cos²θ +cos²θ
= 1
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