2016 · Q63
Consider the following :1. √((1-cosθ)/(1+cosθ)) = cscθ - cotθ2. √((1+cosθ)/(1-cosθ)) = cscθ + cotθ Which of the above is/are identity/ identities?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
For the first expression: √((1−cosθ)/(1+cosθ)) = (1−cosθ)/√(1−cos²θ) = (1−cosθ)/sinθ = cscθ−cotθ. For the second: √((1+cosθ)/(1−cosθ)) = (1+cosθ)/sinθ = cscθ+cotθ. Both identities hold, so option C.