Question

If 2 sin a - 1 = 0, then prove that
sec a + tan a= √3

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Answer 1

$2\sin a-1=0\ \implies\ \sin a=\dfrac{1}{2}$

$\cos a=\sqrt{1-\sin^2\!a}=\sqrt{1-\dfrac{1}{4}}=\sqrt{\dfrac{3}{4}}=\dfrac{\sqrt3}{2}$

Now,

$\begin{aligned}\text{LHS}\implies\ \ &\sec a+\tan a\\\\\implies\ \ &\dfrac{1+\sin a}{\cos a}\\\\\implies\ \ &\dfrac{1+\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\implies\ \ &\dfrac{3}{\sqrt3}\\\\\implies\ \ &\sqrt3\ \ \implies\ \ &\text{RHS}\end{aligned}$

Hence Proved!