Question

From given figure, $\sin x+\sec x+\tan x$ is $\alpha$, find $156\alpha$.

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Answer 1

For the angle $x$ in a right angled $△$,
$\sin x=\frac{Opposite}{Hypotenuse}$,

$\sec x=\frac{Hypotenuse}{Opposite}$ and

$\tan x=\frac{Opposite}{Adjacent}$

From this $△$, we get

So, $\sin x=\frac{5}{13}$, $\sec x=\frac{13}{12}$ and $\tan x=\frac{5}{12}$
Using above values in given expression,

$\Rightarrow \sin x+\sec x+\tan x=\frac{5}{13}+\frac{13}{12}+\frac{5}{12}$

$\Rightarrow \alpha =\frac{294}{156}$

$\Rightarrow 156\alpha =294$