Question

If cosec A = 2, find the value of $\frac{1}{\tan A}+\frac{\sin A}{1+\cos A}$.

Answer 1

Given:

…… (1)

To find:

Now we know is defined as below

Therefore,

Now by substituting the value of from equation (1)

We get,

…… (2)

Now by substituting the value of in the following identity of trigonometry

We get,

Now by taking L.C.M we get

Now by taking square root on both sides

We get,

Therefore,

…… (3)

Now is defined as follows

Now by substituting the value of and from equation (2) and (3) respectively we get,

Therefore,

…… (4)

Now by substituting the value of, and from equation (2) , (3) and (4) respectively we get,

Now by taking L.C.M we get

Now 2 gets cancelled and we get

Now by taking L.C.M, we get,

Now by opening the brackets in the numerator

We get,

Therefore,

Now by taking 2 common

We get,

Now as is present in both numerator as well as denominator, it gets cancelled

Therefore,