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Example 4. Differentiate the following:(i) tan-1|_sin x(1 + cos x

Answer»

Tan^-1 ( sin x / 1 + cos x)

= Tan^-1 ( 2 sin x/2 cos x/2 / 2 cos^2 x/2 )

= Tan^-1 ( sin x/2 / cos x/2 )

= Tan^-1 ( tan x/2 )

= X/2. hence now d/dx(X/2)=1/2



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