Question

Find a numerical value of one trigonometric function of x for cscx = sinx tanx + cosx

Answer 1

Answer:

Step-by-step explanation:

we have

$cscx = sinx tanx + cosx\\\\\frac{1}{sinx}=sinx.\frac{sinx}{cosx} +cosx\\\\\frac{1}{sinx}.sinx.cosx= sinx.\frac{sinx}{cosx}.sinx.cosx+cosx.sinx.cosx\\ cosx= (sinx)^{3} +sinx.(cosx)^{2} \\cosx= sinx[(sinx)^{2}+(cosx)^{2})\\ cosx=sinx.1\\cosx=sinx\\tanx=1\\x=\frac{\pi}{4} +k\pi,k-integer.$