Question

Plz solve question number 5 a (Trigonometric Equations) #salute u if u solved it

Answer 1

$\tan\beta+\cot\beta=2$

Recall that $\cot\beta=\frac1{\tan\beta}$. So if $\tan\beta\neq0$, we can multiply both sides of the equation by $\tan\beta$ to get

$\tan^2\beta+1=2\tan\beta\implies\tan^2\beta-2\tan\beta+1=0$

$\implies(\tan\beta-1)^2=0$

$\implies\tan\beta-1=0$

$\implies\tan\beta=1$

$\implies\boxed{\beta=45^\circ,225^\circ}$