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vats mittal Grade: 12
        





Q.

wat will be d integration of


tan(x-k).tan(x+k).tan2xdx.......???


6 years ago

Answers : (1)

Menka Malguri
39 Points
										

tan2x=tan[(x-k)+(x+k)]


→tan2x=[tan(x-k)+tan(x+k)]/[1-tan(x-k).tan(x+k)]


cross multiplying,we get


tan2x-tan2x.tan(x-k).tan(x+k)=tan(x-k)+tan(x+k)


→tan2x.tan(x-k).tan(x+k)=tan2x-tan(x-k)-tan(x+k)...............(1)


now,


∫tan(x-k).tan(x+k).tan2xdx


=∫[tan2x-tan(x-k)-tan(x+k)]dx......................from(1)


=∫tan2xdx-∫tan(x-k)dx-∫tan(x+k)dx


=(1/2)lnιsec2xι-lnιsec(x-k)ι-lnιsec(x+k)ι+c......where ιxι represents modulus of x,


and convert the soln. further according to the logarithm rules.

5 years ago
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