Question

If cosec θ = 2 show that (cot θ + sinθ/1 + cos θ) = 2

Answer 1

Let us consider a right ∆ABC, right angled at B and ∠C = θ. 

Now, it is given that cosec θ = 2.

Also, sin θ = 1/cosec θ = 1/2 = AB/AC

So, if AB =k, then AC =2k, where k is a positive number. 

Using Pythagoras theorem, we have:

Finding out the other T-ratios using their definitions, we get:

Substituting these values in the given expression, we get:

i.e., LHS = RHS 

Hence proved.