tan x34.sin r cos x

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Solution

The expression to be integrated is given below as,

I= ∫ tanx sinxcosx dx

Simplify the above integral,

I= ∫ tanx ×cosx sinxcosx×cosx dx = ∫ tanx sinx cosx × cos 2 x dx = ∫ tanx tanx cos 2 x dx = ∫ sec 2 x tanx dx

Let tanx=t

Differentiate with respect to t.

sec 2 xdx=dt

By substituting the value, we get

I= ∫ dt t = ∫ t −1/2 dt =[ t −1 2 +1 −1 2 +1 ] =2 t +C

On substituting tanx for t, we get

I=2 tanx +C

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cot 34^{o} - tan 56^{o}

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θ =

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