Question

Prove the following tognometry identittes.
(1 - Cos²A) Cosec²A = 1​

Answer 1

Answer:

Given:-

• (1-Cos²A) Cosec²A= 1

Find:-

• Prove it

Solution:-

(1-Cos²A) Cosec²A= 1

From trigonometry identity ⤵

${ \huge{ \boxed{ \sf{  {sin}^{2} A+ {cos}^{2}A = 1 }}}}$

${ \to{ \sf{(1-Cos²A) Cosec²A= 1}}}$

${ \to{ \sf{(sin²A) \times \frac{1}{sin²A} = 1}}}$

${ \to{ \sf{{ \cancel{sin²A}} \times \frac{1}{{ \cancel{sin²A}}} = 1 }}}$

${ \to{ \sf{1 = 1}}}$

${ \therefore{LHS =RHS }}$

Hence proved ✔