Question

Find the value ofsl theta in each of the following. Theta is an acute angle. I) 3sec2theta=2√3​

Answer 1

$\large{\underline{\underline{\red{\sf{Given:}}}}}$

• $\tt{\theta\:is\:a\:acute\:angle\:.}$
• $\tt{3\sec 2\theta=2\sqrt{3}.}$

$\large{\underline{\underline{\red{\sf{To\: Find:}}}}}$

• $\tt{The\:value\:of\:\theta.}$

$\large{\underline{\underline{\red{\sf{Answer:}}}}}$

$\tt{Given\: that\:\theta\:is\:a\:acute\: angle.}$$\tt{This\:means\:\theta\:lies\:in\:first\: quadrant.}$

$\purple{\bf{Taking\:the\:given\:equ^{n}}}$

$\tt{:\implies 3\sec2\theta=2\sqrt{3}}$

$\tt{:\implies \sec2\theta=\dfrac{2\sqrt{3}}{3}}$

$\tt{:\implies \sec2\theta= \dfrac{2\cancel{\sqrt{3}}}{\cancel{\sqrt{3}}\times\sqrt{3}}}$

$\tt{:\implies \sec2\theta=\dfrac{2}{\sqrt{3}}}$

$\tt{:\implies \sec2\theta=\sec30^{\circ}}$

$\tt{:\implies 2\theta=30^{\circ}}$

$\tt{:\implies \theta=\dfrac{1}{2}\times 30^{\circ}}$

$\underline{\boxed{\green{\tt{\dag \theta =15^{\circ}}}}}$

$\underline{\pink{\tt{Hence\:value\:of\:\theta\:is\:15^{\circ}}}}$