Prove that ∫ cos x/(cos x+ sin x)dx=π/8, x ∈[π/8,3π/8]

Question

Prove that  

\(\int\limits_{\pi/8}^{3\pi/8}\cfrac{cos\,x}{(cos\,x+sin\,x)}dx=\cfrac{\pi}{8}\)

∫ cos x/(cos x+ sin x)dx=π/8, x ∈[π/8,3π/8]

Answer 1

\(y=\int\limits_{\pi/8}^{3\pi/8}\cfrac{cos\,x}{cos\,x+sin\,x}dx\)....(1)

Use King theorem of definite integral

\(y=\int\limits_{\pi/8}^{3\pi/8}\cfrac{sin\,x}{cos\,x+sin\,x}dx...(2)\)

Adding eq.(1) and eq.(2)