prove that cos/1+sin=1-sin/cos
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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
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
priyadharhini:
will u
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I hope it will help you.
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