Question

Differentation of tan2x tan3x tan5x

Answer 1

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Answers Maths A Level
Find the indefinite integral tan(5x)tan(3x)tan(2x)
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1376 views 1 year ago
Noticing that tan(5x) = tan(3x+2x) we use the tan compound angle formula to find tan(5x) = (tan(2x)+tan(3x))/(1-tan(2x)tan(3x)) and thus tan(5x)tan(3x)tan(2x) = tan(5x)-tan(3x)-tan(2x). From then we can integrate the parts of the sum individually as normal. Remembering that if F(x) = integral of f(x) dx then the integral of f(ax) dx = 1/a F(ax)

Answer 2

$\tan( 2\alpha ) = \frac{2 \tan( \alpha ) }{1 - { \tan( \alpha ) }^{2} } \\ \tan(3 \alpha ) = \frac{3 \tan( \alpha ) - { \tan( \alpha ) }^{3} }{1 - 3 { \tan( \alpha ) }^{2} } \\ \tan(5 \alpha ) = \tan(3 \alpha + 2 \alpha )$
That's the differentatio of tan 2x,tan3x,tan5x