If cotθ=abcotθ=abcotθ=ab and 90∘>θ>0∘,90∘>θ>0∘,90∘>θ>0∘, find value of cosecθ.cosecθ.cosecθ.
Answer:
√b2+a2b2√b2+a2b2√b2+a2b2
- We know that,
cosecθ=√(1+cot2θ)cosecθ=√(1+cot2θ)cosecθ=√(1+cot2θ) - Now replace value of cotθcotθcotθ in above equation.
cosecθ=√1+(ab)2cosecθ=√1+(ab)2cosecθ=√1+(ab)2 - Simplify RHSRHSRHS of above equation.
cosecθ=√b2+a2b2cosecθ=√b2+a2b2cosecθ=√b2+a2b2