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Prove that: (1+sinA-cosA)/(1+sinA+cosA...

Prove that:
`(1+sinA-cosA)/(1+sinA+cosA)=tan(A/2)`

Text Solution

Verified by Experts

LHS `=(1+sinA-cosA)/(1+sinA+cosA)=((1-cosA)+sinA)/((1+cosA)+sinA)`
`=(2sin^(2)A/2+2sinA/2cosA/2)/(2cos^(2)A/2+2sinA/2cosA/2)`
`=(sinA/2(sinA/2cosA/2))/(cosA/2(cosA/2+sinA/2))`
`=(sinA/2)/(cosA/2)=tanA/2`= RHS Hence proved.
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