Question

Find the value of $se{c}^2(ta{n}^{-1}2)+cose{c}^2(co{t}^{-1}3)$

• A. $12$
• B. $5$
• C. $15$
• D. $9$

Answer 1

Answer: (C)

$se{c}^2(ta{n}^{-1}2)+cose{c}^2(co{t}^{-1}3)$
$={\left[sec\left(ta{n}^{-1}2\right)\right]}^2+{\left[cosec\left(co{t}^{-1}3\right)\right]}^2$
$={\left[sec\left(se{c}^{-1}\sqrt{5}\right)\right]}^2+{\left[cosec\left(cose{c}^{-1}\sqrt{10}\right)\right]}^2$
$={\left(\sqrt{5}\right)}^2+{\left(\sqrt{10}\right)}^2=5+10=15$