Prove . sin^3 A+cos^3 A/1-2cos^2 A

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Solution

(sin³x+cos³x)/(1-2cos²x)

= (sinx+cosx)(sin²x - sinx cosx +cos²x)/(sin²x-cos²x)

= (sinx+cosx)(1 - sinx cosx)/[(sinx-cosx)(sinx +cosx)]

= (1 - sinx cosx)/(sinx-cosx)

= (1/cosx-sin x)/(tanx-1)
= (sec x- sinx)/(tanx -1)

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