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Trigonometric Ratios of Compound Angles

Prove thatCos...

Question

Prove that

Cosα/(1+sinα)+sinα/(1+cosα)=2secα

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Solution

(cos(x)1+sin(x))+(1+sin(x)cos(x))
=cos2(x)+1+2sin(x)+sin2(x)cos(x)(1+sin(x)
=2+2sin(x)cos(x)(1+sin(x))
=2cos(x)
=2⋅1cos(x)
=2secx
(I have taken theeta =x.)

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