By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x – 4 sin'x. Hence, prove that sin'x dx 24

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A: Image is attached with detailed solution.

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A: Introduction :

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A: put 2x=u so that dx=1/2 du.and solve the question.

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Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x - 4 sin°x.…

A: Evaluation of the definite Integral

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A: Given: tanx=-16,   cosx>0 sin2x can be calculated as, sin2x=2tanx1+tan2x          =2×-161+-162…

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Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

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A: sinx-cosx2=sin2x-2sinxcosx+cos2x     ∵a-b2=a2-2ab+b2=sin2x+cos2x-2sinxcosx=1-sin2x…

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