If cot θ+cosec θ=√2 cot θ, show that cot θ−cosec θ=√2 cosec θ
Answer:
- We have cot θ+cosec θ=√2 cot θ By squaring both the sides, we get (cot θ+cosec θ)2=(√2 cot θ)2⟹cot2 θ+cosec2 θ+2 cot θ cosec θ=2 cot2 θ⟹cosec2 θ=2 cot2 θ−cot2 θ−2 cot θ cosec θ⟹cosec2 θ+cosec2 θ=cot2 θ−2 cot θ cosec θ+cosec2 θ [ Adding cosec2 θ on both the sides. ]⟹2 cosec2 θ=(cot θ−cosec θ)2⟹cot θ−cosec θ=√2 cosec θ
- Hence, cot θ−cosec θ=√2 cosec θ.