Question

if y=1+sinx-cosx/1+sinx+cosx

show that , dy/dx=1/1+cosx​

Answer 1

Answer:

Given,

y=1+sinx-cox/1+sinx+cosx=sinx+(1-cosx) /sinx+(1+cosx)

or, y=2sinx/2cosx/2+2sin²x/2 / 2sinx/2 cosx/2 +2cos²x/2

=2sinx/2 (cos x/2+sin x/2) / 2cos x/2(sinx/2 +cosx/2)=tan x/2

:.dy/dx=sec² x/2.1/2=1/2cos²x/2=1/1+cosx

(prove)

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