Question

If tan $\frac{\varphi }{2}$ = 2,find the value of $\frac{5}{4}sin\varphi$.

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Answer 1

We will use the relation $sin\varphi =\frac{2tan\frac{\varphi }{2}}{1+ta{n}^2\frac{\varphi }{2}}$

$\Rightarrow$ $sin\varphi$ = $\frac{2\times 2}{1+2^2}$ = $\frac{4}{5}$

$\Rightarrow$ $\frac{5}{4}sin\varphi$ = $\frac{2\times 2}{1+2^2}$ = $\frac{4}{5}$

$\Rightarrow$ $\frac{5}{4}sin\varphi$ = 1