What is \(\rm \cot{\frac{A}{2}}+ \tan {\frac{A}{2}}\) equal to?1. 2

1.	What is \(\rm \cot{\frac{A}{2}}+ \tan {\frac{A}{2}}\) equal to?1. 2 sec A2. 2 cosec A3. sin A4. sec A
Answer» Correct Answer - Option 2 : 2 cosec A Concept: sin² θ + cos² θ = 1. sin 2θ = 2 sin θ cos θ. Calculation: Consider the expression \(\rm \cot{\frac{A}{2}}+ \tan {\frac{A}{2}}\). = \(\rm \frac{\cos\frac{A}{2}}{\sin\frac A2}+ \frac{\sin \frac{A}{2}}{\cos\frac{A}{2}}\) = \(\rm \frac{\cos^2\frac{A}{2}+\sin^2\frac{A}{2}}{\sin\frac A2\cos\frac{A}{2}}\) = \(\rm \frac{1}{\sin\frac A2\cos\frac{A}{2}}\) = \(\rm \frac{2}{2\sin\frac A2\cos\frac{A}{2}}\) = \(\rm \frac {2}{\sin A}\) = 2 cosec A

What is \(\rm \cot{\frac{A}{2}}+ \tan {\frac{A}{2}}\) equal to?1. 2 sec A2. 2 cosec A3. sin A4. sec A

Answer» Correct Answer - Option 2 : 2 cosec A

Concept:

Calculation:

Consider the expression \(\rm \cot{\frac{A}{2}}+ \tan {\frac{A}{2}}\).

= \(\rm \frac{\cos\frac{A}{2}}{\sin\frac A2}+ \frac{\sin \frac{A}{2}}{\cos\frac{A}{2}}\)

= \(\rm \frac{\cos^2\frac{A}{2}+\sin^2\frac{A}{2}}{\sin\frac A2\cos\frac{A}{2}}\)

= \(\rm \frac{1}{\sin\frac A2\cos\frac{A}{2}}\)

= \(\rm \frac{2}{2\sin\frac A2\cos\frac{A}{2}}\)

= \(\rm \frac {2}{\sin A}\)

= 2 cosec A