(4) cot^20 - tan^20 = cosec^20 - sec²0
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Answer:
Cot^2 0 - Tan^2 0 = Cosec ^2 0 - Sec^2 0
LHS:-
cos^2 0 - sin^2 0
sin 0^2 cos^2 0
cos^4 0 - sin^4 0
sin^2 0 cos^2 0
(cos^2 0 + sin^2 0)(cos^2 0 - sin^2 0)
sin^2 0 cos^2 0
1 (cos^2 0 - sin^2 0)
sin^2 0 cos^2 0
cos^2 - sin^2 0
sin^2 0 cos^2 0 sin^2 0 cos^2 0
1 - 1
sin^20 cos^2 0
Cosec ^2 0 - Sec^2 0
LHS = RHS
Hence proved.
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