If $\sin A=\frac{1}{2}, A$ is an acute angle, then find the value of $\frac{\tan A-\cot A}{\sqrt{3}(1+{cosec} A)}$.
Answer & explanation
Correct answer: option 3
We are given that :-
sinA = \(\frac{1}{2}\)
{ we know , sin 30º = \(\frac{1}{2}\) }
So, A = 30º
Now,
\(\frac{tanA - cotA}{ √3 ( 1 + cosecA ) }\)
= \(\frac{tan 30º - cot 30º}{ √3 ( 1 + cosec 30º ) }\)
= \(\frac{ 1/ √3 - √3}{ √3 ( 1 + 2 ) }\)
= \(\frac{ -2/ √3}{ 3√3 }\)
= \(\frac{ -2}{ 9 }\)