If α+β=90∘α+β=90∘, simplify √cosαcosecβ−cosαsinβ.√cosαcosecβ−cosαsinβ.
Answer:
±sinα±sinα
- It is given that α+β=90∘α+β=90∘
⟹β=90∘−α⟹β=90∘−α - Replace ββ with 90∘−α90∘−α in given expression.
√cosαcosecβ−cosαsinβ=√cosαcosec(90∘−α)−cosαsin(90∘−α)=√cosαsecα−cosαcosα=√1−cos2α=±sinα