Question

Find the exact value. if the expression is undefined write undefined. csc 135°

Answer 1

$\bf csc(\theta)=\cfrac{1}{sin(\theta)}\\\\ -----------------------------\\\\ csc(135^o)\implies \cfrac{1}{sin(135^o)}\implies \cfrac{1}{\frac{\sqrt{2}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{2}}{2}}\implies \cfrac{1}{1}\cdot \cfrac{2}{\sqrt{2}}\implies \cfrac{2}{\sqrt{2}} \\\\\\ \textit{now, rationalizing the denominator} \\\\\\ \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{(\sqrt{2})^2}\implies \cfrac{2\sqrt{2}}{2}\implies \boxed{\sqrt{2}}$

Answer 2

Cosec 135 = cosec 45 which is square root of 2.