If $\sin heta + \cos heta = \sqrt{3}$, then prove that $ an heta + \cot heta = 1$.

Question

If $\sin 	heta + \cos 	heta = \sqrt{3}$, then prove that $	an 	heta + \cot 	heta = 1$.

Accepted Answer

Step 1: $\sin 	heta + \cos 	heta = \sqrt{3}$
Squaring: $\sin^2 	heta + \cos^2 	heta + 2\sin 	heta \cos 	heta = 3$
$\Rightarrow \sin 	heta \cos 	heta = 1$
Step 2: LHS $= 	an 	heta + \cot 	heta = \frac{\sin 	heta}{\cos 	heta} + \frac{\cos 	heta}{\sin 	heta} = \frac{\sin^2 	heta + \cos^2 	heta}{\sin 	heta \cos 	heta} = \frac{1}{1} = 1 = $ RHS

Question

Solution