Question

Tan theta+Sin theta/Tan theta-Sin theta=Sec theta+1/Sec theta-1
Prove it

Answer 1

(tan+sin)/(tan-sin)={(sin/cos)+sin}/{(sin/cos)-sin}=(sin+sincos)/sin/(sin-sincos)/sin={sin(1+cos)}/{sin(1-cos)}=(1+cos)/(1-cos)=(1+1/sec)/(1-1/sec)=(sec+1)/sec/(sec-1)/sec=(sec+1)/(sec-1).......

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