(sec A(sec A + tan A)(1 - sin A))/((cosec² A-1)sin² A) is equal to:

(sec A(sec A + tan A)(1 - sin A))/((cosec² A-1)sin² A) is…

$\frac{sec A(sec A + tan A)(1 - sin A)}{(cosec^2 A-1)sin^2 A}$ is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. sec² A.

On solving the numerator part first,

= SecA(SecA + TanA)(1 - SinA)

= 1/CosA(1/CosA + SinA/CosA)(1 - SinA)

= (1 + SinA)/Cos²A × (1 - SinA)

= 1.

Now solve the denominator part,

= (Cosec²A - 1)Sin²A

= (1 - Sin²A)

= Cos²A

On combining,

= 1/Cos²A

= Sec²A