Question

solve tan(theta)+sec(theta)=root3

Answer 1

Answer:

$\theta = 30\degree$

Step-by-step explanation:

$Given \\ tan\theta+sec\theta=\sqrt{3}\:---(1)$

$We\: know\: the \\ trigonometric \:identity :\\sec^{2}\theta-tan^{2}\theta=1$

$\implies (sec\theta+tan\theta)(sec\theta-tan\theta)=1$

$\implies \sqrt{3}\times (sec\theta-tan\theta)=1$

$\implies sec\theta-tan\theta=\frac{1}{\sqrt{3}}\:---(2)$

/* Add equations (1) and (2) ,we get

$2sec\theta = \sqrt{3}+\frac{1}{\sqrt{3}}$

$\implies 2sec\theta= \frac{3+1}{\sqrt{3}}$

$\implies sec\theta=\frac{4}{\sqrt{3}\times 2}$

$\implies sec\theta=\frac{2}{\sqrt{3}}$

$\implies sec\theta=sec 30\degree$

$\implies \theta = 30\degree$

Therefore,

$\theta = 30\degree$

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