Question

Evaluate this problem step by step sin90⁰+3tan²60⁰÷cos²30⁰

Answer 1

$\huge \sf{\underline{Solution :- }}$

$\sin90° + 3 \tan^{2} 60° \div \cos^{2} 30°$

$= 1 + 3 \times {( \sqrt{3} })^{2} \div( { \frac{ \sqrt{3} }{2} })^{2}$

$= 1 + 3 \times 3 \div \frac{3}{4}$

$= 1 + 3 \times 3 \times \frac{4}{3}$

$= 1 + 3 \times 4$

$= 1 + 12$

$= 13$

$\bf \red{Answer : 13.}$

$\sf \pink {\underline{Important \: Informations:-}}$

$• \: \sin0 \degree = 0$

$• \: \sin30 \degree = \frac{1}{2}$

$• \: \sin45 \degree = \frac{1}{ \sqrt{2}}$

$• \: \sin60 \degree = \frac{ \sqrt{3} }{2}$

$• \: \sin90 \degree = 1$

$• \: \cos0 \degree = 1$

$• \: \cos30 \degree = \frac{ \sqrt{3} }{2}$

$• \: \cos45 \degree = \frac{1}{ \sqrt{2} }$

$• \: \cos60 \degree = \frac{1}{2}$

$• \: \cos90 \degree = 0$

$• \: \tan0 \degree = 0$

$• \: \tan30 \degree = \frac{1}{ \sqrt{3} }$

$• \: \tan 45\degree = 1$

$• \: \tan60 \degree = \sqrt{3}$

$• \: \tan90 \degree = \infty$

$• \: \cot0 \degree = \infty$

$• \: \cot30 \degree = \sqrt{3}$

$• \: \cot 45\degree = 1$

$• \: \cot60 \degree = \frac{1}{ \sqrt{3} }$

$• \: \cot90 \degree = 0$

$• \: \sec0\degree = 1$

$• \: \sec30\degree = \frac{2}{ \sqrt{ 3} }$

$• \: \sec45\degree = \sqrt{2}$

$• \: \sec60\degree = 2$

$• \: \sec90\degree = \infty$

$• \: \cosec0\degree = \infty$

$• \: \cosec30\degree = 2$

$• \: \cosec45\degree = \sqrt{2}$

$• \: \cosec60\degree = \frac{2}{ \sqrt{3} }$

$• \: \cosec90\degree = 1$