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Question Number 67345 by Aditya789 last updated on 26/Aug/19

$$3sinx+5cosx=5thenprovethat$$$$5sinx-3cox=+3$$

Answered by $@ty@m123 last updated on 26/Aug/19

$$\frac{3}{5}\sin x+\cos x=1$$$$\frac{1-\cos x}{\sin x}=\frac{3}{5}$$$$\frac{1-\cos x}{\sin x}\times \frac{1+\cos x}{1+\cos x}=\frac{3}{5}$$$$\frac{1-\cos {}^{2}x}{\sin x(1+\cos x)}=\frac{3}{5}$$$$\frac{\mathrm{s}in{}^{2}x}{\sin x(1+\cos x)}=\frac{3}{5}$$$$\frac{\sin x}{1+\cos x}=\frac{3}{5}$$$$5\sin x=3+3\cos x$$$$5sinx-3cosx=3$$

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