Question

prove: 1+sinO/cosO + cosO/1+sinO = 2secO​

Answer 1

Answer:

hope you will understand it.

Answer 2

$1 + \sin( \alpha ) \div \cos( \alpha ) + \cos( \alpha ) \div 1 + \sin( \alpha ) \\ \\ = {(1 + \sin( \alpha ) )}^{2} + { \cos( \alpha ) }^{2} \div \sin( \alpha ) (1 + \cos( \alpha ) ) \\ \\ = 1 + { \sin( \alpha ) }^{2} + 2 \sin( \alpha ) + { \cos( \alpha ) }^{2} \div (1 + \sin( \alpha ) )\cos( \alpha ) \\ \\ = 2(1 + \sin( \alpha ) \cos( \alpha ) ) \div (1 + \sin( \alpha )) \cos( \alpha) \\ \\ = 2 \div \cos( \alpha ) \\ \\ = 2 \sec( \alpha )$

sin²a + cos²a = 1

seca = 1/cosa

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