Question

If $\sin \theta =\frac{3}{5}$, evaluate $\frac{\cos \theta -{\displaystyle \frac{1}{\tan \theta }}}{2\cot \theta }$.

Answer 1

Given: ……(1)

To find the value of

Now, we know the following trigonometric identity

Therefore, by substituting the value of from equation (1) ,

We get,

Therefore,

Now by taking L.C.M

We get,

Therefore by taking square root on both sides

We get,

Therefore,

…… (2)

Now, we know that

Therefore by substituting the value of and from equation (1) and (2) respectively

We get,

…… (3)

Also, we know that

Therefore from equation (4) ,

We get,

Therefore,

…… (4)

Now, by substituting the value of, and from equation (2) , (3) and (4) respectively in the expression below

We get,

Therefore,