Question

Express trigonometric function sin A in terms of cot A
A. $\dfrac{{\sqrt {1 + {{\cot }^2}A} }}{{\cot A}}$
B. $\sqrt {\dfrac{{1 + {{\cot }^2}A}}{{\cot A}}} $
C. $\dfrac{1}{{\sqrt {1 + {{\cot }^2}A} }}$
D. $\dfrac{{\sqrt {1 - {{\cot }^2}A} }}{{\cot A}}$

Answer 1

Hint-In this particular type of question express the formula of cosec$\theta $ and cot$\theta $ to get the relation between them. Then use $\sin A = \dfrac{1}{{\cos ecA}}$ and trigonometric identities to get to the required answer.

Complete step-by-step answer:
We know that
 $\cos e{c^2}A = 1 + {\cot ^2}A$
$ \Rightarrow \cos ecA = \sqrt {1 + {{\cot }^2}A} $
Also , $\sin A = \dfrac{1}{{\cos ecA}}$
$ \Rightarrow \sin A = \dfrac{1}{{\sqrt {1 + {{\cot }^2}A} }}$

Note-Note that this question is required to find the relation between sin$\theta $ and cot$\theta $ . The formulas leading to the solution should be recalled in such types of questions . Note that any one trigonometric function is being converted to solve such types of questions thus formulas play an important role in the solution.