Question

Find the value of $\frac{sin(-{660}^0)tan\left({1050}^0\right)sec(-{420}^0)}{cos\left({225}^0\right)cosec\left({315}^0\right)cos\left({510}^0\right)}$

Answer 1

$\frac{sin(-660)tan\left(1050\right)sec(-420)}{cos\left(225\right)cosec\left(315\right)cos\left(510\right)}$
$=\frac{-sin\left(660\right)tan\left(1050\right)sec\left(420\right)}{cos\left(225\right)cosec\left(315\right)cos\left(510\right)}$
$=\frac{-sin(360+300)tan(1080-30)sec(360+60)}{cos(270-45)cosec(360-45)cos(360+150)}$
$=\frac{-sin300(-tan(30\left)\right)sec60}{-sen45(-cosec45)cos150}$
$=\frac{sin(360-60)\left(\frac{1}{\sqrt{3}}\right)\left(2\right)}{\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)cos(90+60)}$
$=\frac{-sin60\times \frac{2}{\sqrt{3}}\times 2}{\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\times (-sin60)}$
$=\frac{2}{\sqrt{3}}\times 2=\frac{4}{\sqrt{3}}$