Q9 of 104 Page 204

Prove the following by using trigonometric identities:

2sec2θ — sec4θ — 2cosec2θ + cosec4θ = cot4θ — tan4θ.

2sec2θ — sec4θ — 2cosec2θ + cosec4θ

= 2(1 + tan2θ) – (1 + tan2θ)2 – 2(1 + cot2θ) + (1 + cot2θ)2


open all the brackets and cancel terms


= cot4θ – tan4θ


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