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The value of 1+sin theta- cos theta/1+Sin theta+cos theta is ​ ​ ​

The value of 1+sin theta- cos theta/1+Sin theta+cos theta is
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Grade:8

2 Answers

Arun
25757 Points
5 years ago
L.H.S = 1+sinx-cosx/1+sinx+cosx 
= 1+sinx-cosx(1+sinx+cosx)/1+sinx+cosx(1+s... 
=(1+sinx)^2-(cosx)^2/(1+sinx+cosx)^2 
=2sinx+2sin^2x/2+2sinx+cosx+2sinxcosx 
=2sinx(1+sinx)/2(1+sinx)+2cosx(1+sinx) 
=sinx/2cosx 
= tanx/2
Suraj Kumar
49 Points
5 years ago
On multiplying the numerator and denominator by (1+sinx+cosx) We get (1+sinx)^2-cos^2/(1+sinx +cosx)^2=(1+sin^2x+2sinx-cos^2x)/(1+sin^x+cos^2x+2sinx+2cosx+2sinx×cosx)=(2sinx+2sin^2x)/(1+1+2sinx+2cosx+2simx×cosx)=2sinx (1+sinx)/2(1+sinx)+2cosx (1+sinx)=2sinx (1+sinx)÷2 (1+sinx)[1+cosx]=Sinx/1+cosx

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