Question

Hey guys!!!
Please solve..
The best one will be marked as the brainliest ..

Answer 1

Step-by-step explanation:

Important Formulas:

(i) sin²θ + cos²θ = 1

(ii) sec²θ = 1 + tan²θ

(iii) cosec²θ = 1 + cot²θ

For the better understanding I am replacing θ with A.

LHS:

$Given:\frac{cot^2A(secA-1)}{sinA+1}$

$=\frac{cot^2A*(secA-1)*(\frac{secA+1}{secA+1})}{(1+sinA)*(\frac{1+sinA}{1-sinA})}$

$=\frac{cot^2A(\frac{sec^2A-1)}{secA+1})}{(\frac{1-sin^2A}{1-sinA})}$

$=cot^2A(\frac{sec^2A-1}{secA+1})(\frac{1-sinA}{1-sin^2A})$

$=\frac{cot^2A(tan^2A)(1-sinA)}{(secA+1)(cos^2A)}$

$=\frac{cot^2A * \frac{1}{cot^2A} * (1-sinA)}{(secA + 1)(\frac{1}{sec^2A})}$

$=\frac{sec^2A(1-sinA)}{secA+1}$

$=\boxed{sec^2A(\frac{1-sinA}{1+secA})}$

Hope it helps!

Answer 2

The answer is explained