Simplify √1+cosθ1−cosθ.
Answer:
cosecθ+cotθ
- We know that 1−cos2θ=sin2θ. Using this identity we can simplify the denominator by multiplying it by 1+cosθ.
- Now, on multiplying numerator and denominator by 1+cosθ,
√1+cosθ1−cosθ=√1+cosθ1−cosθ×1+cosθ1−cosθ=√(1+cosθ)21−cos2θ=√(1+cosθ)2sin2θ=1+cosθsinθ=1sinθ+cosθsinθ=cosecθ+cotθ