Question

If sin A − cosec A = 2, the value of sin² A + cosec² A is ______.

Options

• 2

• 0

• 4

• 6

Answer 1

If sin A − cosec A = 2, the value of sin² A + cosec² A is 6.

Explanation:

Given sin A − csc A = 2. Since \[\csc A = \frac{1}{\sin A}\], we can square both sides of the equation:

\[\left(\sin A - \frac{1}{\sin A}\right)^2 = 2^2\]

\[\sin^2 A + \frac{1}{\sin^2 A} - 2(\sin A)\left(\frac{1}{\sin A}\right) = 4\]

sin² A + csc² A − 2 = 4

sin² A + csc² A = 4 + 2

∴ sin² A + csc² A = 6