1.

What is the simplified value of \(\sqrt {\frac{{\sec A}}{{\sec A - 1}} + \frac{{\sec A}}{{\sec A + 1}}?} \)1). cosec A2). √2 cosec A3). 2 sec2A4). sec A

Answer»

We can WRITE sec A = 1/ COS A, Now it can be written as

⇒ √{1/(1 - cos A) + 1/(1 + cos A) }

⇒ √[{(1 - cos A) + (1 + cos A) }/{(1 - cos A) (1 + cos A) }]

⇒ √{2/(1 - cos2A) } since we know that 1 - cos2 A = sin2 A

⇒ √2/sin A = √2 COSEC A

∴ Its simplified VALUE is √2 cosec A



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