$\sqrt{\frac{1 + c o s A}{1 - c o s A}}$ = ?

(a) cosec A - cot A (b) cosec A + cot A

(c) cosec A cot A (d) none of these

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Solution

LHS- $\sqrt{\frac{1 + c o s A}{1 - c o s A}}$

Multiplying with $\sqrt{1 + c o s A}$ on both numerator and denominator, we have,

= $\sqrt{\frac{1 + c o s A}{1 - c o s A} \times \frac{1 + c o s A}{1 + c o s A}}$

= $\sqrt{\frac{(1 + c o s A)^{2}}{1 - c o s^{2} A}}$

= $\frac{1 + c o s A}{\sqrt{s i n^{2} A}}$
= $\frac{1 + c o s A}{s i n A}$

= $\frac{1}{s i n A}$ + $\frac{c o s A}{s i n A}$

=cosecA + cotA

(b)

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