Question

Cot theta+tan theta=k, where theta is an acute angle and k is a constant, has real value of tan theta, show that k«2 or k»2?

Answer 1

`cos theta+tantheta=k`, where `0^o<=theta<=90^o`

Let `theta=0^o`,

`cos 0^o +tan0^o=1`,

Let `theta=90^o`,

`cos90^o +tan90^o=oo`

Hence, this equation satisfies all real values of `k`.