Question

Evaluate \(\sqrt {\frac {1 – sin⁡ \, ⁡A}{1 + sin \, ⁡⁡A}}\).

(a) cos A + tan A

(b) cos A – tan A

(c) tan A – cot A

(d) sec A + tan A

This question was posed to me in unit test.

This intriguing question comes from Trigonometric Identities in section Trigonometry of Mathematics – Class 10

Answer 1

Correct option is (d) sec A + tan A

Best explanation: \(\sqrt {\frac {1 – sin⁡ \, ⁡A}{1 + sin⁡ \, ⁡A}} = \sqrt {\frac {1 – sin⁡ \, ⁡A}{1 + sin \, ⁡⁡A}} . \sqrt {\frac {1 – sin \, ⁡A}{1 – sin \, ⁡⁡A}}\)

= \(\frac {\sqrt {(1 + sin \, ⁡A)^2}}{\sqrt {1 – sin^2} \, ⁡A} \)

= \(\frac {1 + sin⁡ \, ⁡A}{\sqrt {cos^2} \, ⁡A}\)     (∵ sin^2 A + cos^2 A = 1)

= \(\frac {1 + sin⁡ \, ⁡A}{cos⁡ \, ⁡A}\)

= sec A + tan A