Simplify: cosec2θ(cosθ−11+cosecθ)−tan2θ(cosecθ−11+cosθ)
Answer:
0
- On adding two fractions:
cosec2θ(cosθ−11+cosecθ)−tan2θ(cosecθ−11+cosθ)=cosec2θ(cosθ−1)(cosθ+1)−tan2θ(cosecθ−1)(cosecθ+1)(1+cosecθ)(1+cosθ)=cosec2θ(cos2θ−1)−tan2θ(cosec2θ−1)(1+cosecθ)(1+cosθ)=cosec2θsin2θ−tan2θcot2θ(1+cosecθ)(1+cosθ)=1−1(1+cosecθ)(1+cosθ)=0