Question

(1+sinx/cosx)+(cosx/1+sin)

Answer 1

( 1 + sinx / cosx ) + ( cosx / 1 + sinx ) =

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(1 + sinx)(1 + sinx)/cosx(1 + sinx)

+

(cosx)(cosx)/(1 + sinx)(cosx) =

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(1 + sinx)^2 /cosx(1 + sinx)

+

(cosx)^2/cosx(1 + sinx) =

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1 + 2sinx + sin^2 x/cosx(1 + sinx)

+

cos^2 x/cosx(1 + sinx) =

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1 + sin^2 x + cos^2 x + 2sinx / cosx(1 + sinx) =

Hint :

Sin^2 x + Cos^2 x = 1

1 + 1 + 2sinx / cosx(1 + sinx) =

2 + 2sinx / cosx(1 + sinx) =

2(1 + sinx)/cosx(1 + sinx) =

( 1 + sinx) simplifies from the face and the denominator of the fraction

2/cosx