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problem on integration using reduction formulae

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 show that (m+n)I(m,n) = m I(m -1,n-1) + (cosx)^m*sin (nx)
where I(m,n ) = ∫ (cosx)^m * cos (nx) dx
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use integration by parts for one step and then
try to change sinxsin(nx) and
 extract cosnx using the formulae
for cos(nx-x) since n-1 is hinted to in the question
 answer and  some steps are given below
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(trig. formulae) 





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