Question

$cos \div 1 + sin + 1 + sin \div cos$
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Answer 1

The question should be "prove that cos A/ 1+sinA + 1+sin A / cos A = 2 tanA." Let me show you how.

cosA/1+sinA + 1+sinA/cosA

= cos2A + 1 + 2sinA + sin2A/cosA + cosA*sinA

=> cos2A + sin2A - cos2A + 2sinA + sin2A/cosA(1+sinA) [since 1 = sin2A-cos2A]

=> 2sin2A + 2sinA/cosA(1+sinA)

=>2sinA(sinA+1)/cosA(1+sinA)

= 2sinA/cosA

= 2 tanA