Question

(ii) cos^4 alpha + 2 cos^2 alpha (1-1/sec^2 alpha)​

Answer 1

Let A=Alpha,

LHS;

= (cos^2A)^2 + 2cos^2A (1-cos^2A)

= (1-sin^2A)^2 + 2cos^2A (sin^2A)

= 1+sin^4A-2sin^2A +2(1-sin^2A)(sin^2A)

= 1+sin^4A-2sin^2A +2(sin^2A - sin^4A)

= 1+sin^4A-2sin^2A +2sin^2A-2sin^4A

= 1-sin^4A =RHS

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