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Question

Show that cos4α+2cos2α(11sec2α)=1sin4α

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Solution

LHS=cos4α+2cos2α(11sec2α)
=cos4α+2cos2α(1cos2α)
=cos4α+2cos2α2cos4α
=2cos2αcos4α
=cos2α(2cos2α)
=(1sin2α)(21+sin2α)
=(1sin2α)(1+sin2α)
=1sin4α
=RHS
Hence proved.

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