Question

If $5\sin \theta =4$, prove that $\frac{1}{\cos \theta }+\frac{1}{\cot \theta }=3$.

Answer 1

Given $5\sin \theta =4\to \sin \theta =\frac{4}{5}$

So $\sqrt{5^2-4^2}$

$=\sqrt{25-16}=\sqrt{9}=3$

So $\cos \theta =\frac{3}{5}$

$\cot \theta =\frac{\cos \theta }{\sin \theta }=\frac{3}{5}\times \frac{5}{4}=\frac{3}{4}$

So $\frac{1}{\cos \theta }+\frac{1}{\cot \theta }=3$

$\frac{5}{3}+\frac{4}{3}=3$

$\frac{9}{3}=3$

$3=3$