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Question Number 80113 by jagoll last updated on 31/Jan/20

$$howdoyousimply$$$$\sin ({\tan }^{-1}\left(3x\right)+{\cos }^{-1}\left(x\right))?$$

Commented by john santu last updated on 31/Jan/20

$$letx=\cos t,3x=\tan y$$$$\Rightarrow \sin y\cos t+\cos y\sin t$$$$=\frac{3x^2}{\sqrt{1+9x^2}}+\frac{\sqrt{1-x^2}}{\sqrt{1+9x^2}}$$$$=\frac{3x^2+\sqrt{1-x^2}}{\sqrt{1+9x^2}}$$

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