Question

prove that sin/1-cos+tan/1+cos=cot +sec×cosec​

Answer 1

$\underline{\texttt{Solution :}}$

$\mathtt{Now,\:L.H.S.=\frac{sinQ}{1-cosQ}+\frac{tanQ}{1+cosQ}}$

$\mathtt{=\frac{sinQ(1+cosQ)+tanQ(1-cosQ)}{(1-cosQ)(1+cosQ)}}$

$\mathtt{=\frac{sinQ+sinQ\:cosQ+tanQ-tanQ\:cosQ}{1-cos^{2}Q}}$

$\mathtt{=\frac{sinQ+sinQ\:cosQ+\frac{sinQ}{cosQ}-\frac{sinQ}{cosQ}\:cosQ}{sin^{2}Q}}$

$\mathtt{=\frac{sinQ+sinQ\:cosQ+\frac{sinQ}{cosQ}-sinQ}{sin^{2}Q}}$

$\mathtt{=\frac{sinQ\:cosQ+\frac{sinQ}{cosQ}}{sin^{2}Q}}$

$\mathtt{=\frac{sinQ\:cosQ}{sin^{2}Q}+\frac{\frac{sinQ}{cosQ}}{sin^{2}Q}}$

$\mathtt{=\frac{cosQ}{sinQ}+\frac{1}{cosQ\:sinQ}}$

$\mathtt{=cotQ+secQ\:cosecQ=R.H.S.}$

$\mathtt{Hence,\:proved.}$

Answer 2

Hope it helps..............