Question

Can u solve it pls........

Answer 1

$\huge\bold{Solution}$

$\huge\bold{Prove\: That}$

$\frac{sin∅}{1 - Cos∅} + \frac{Tan∅}{1 + Cos∅}$ = Cot∅ + Sec∅.Cosec∅

$\small\bold{LHS}$

=> $\frac{Sin∅}{1 - Cos∅} + \frac{Tan∅}{1 + Cos∅}$

=> $\frac{Sin∅(1 + Cos∅) + Tan∅(1 - Cos∅)}{(1)² - (Cos∅)²}$

=> $\frac{Sin∅ + Sin∅Cos∅ + Tan∅ - Tan∅Cos∅}{1 - Cos²∅}$

=> $\frac{Sin∅ + Sin∅Cos∅ + Tan∅ - Sin∅}{1 - Cos²∅}$.

=> $\frac{Sin∅Cos∅ + Tan∅}{1 - Cos²∅}$

=> $\frac{Sin∅Cos∅ + Tan∅}{Sin²∅}$

=> $\frac{Sin∅Cos∅}{Sin²∅} + \frac{Tan∅}{Sin²∅}$

=> $\frac{Cos∅}{Sin∅} + /frac{1}{Cos∅Sin∅}$

We can also write it as

=> Cot∅ + Sec∅Cosec∅

LHS = RHS

Hence Proved✔

Hope it helps u out✔✔