Question

if $Sin\theta =\frac{3}{5}$ what is the value of ${(\tan \theta +\sec \theta )}^2$?

• A. $2$
• B. $3$
• C. $4$
• D. $-4$

Answer 1

Answer: (C)

$4$

$Sin\theta =\frac{P}{H}=\frac{3}{5}$

According to the Pythagorean therom

$H^2=B^2+P^2$

$\Rightarrow B=\sqrt{h^2-p^2}$
$\Rightarrow B=\sqrt{5^2-3^2}$

$\Rightarrow B=\sqrt{16}$

$\Rightarrow B=4cm$

$\therefore tan\theta =\frac{P}{B}=\frac{3}{4}$

$sec\theta =\frac{H}{B}=\frac{5}{4}$

$\therefore (tan\theta +sec\theta {)}^2=(\frac{3}{4}+\frac{5}{4}{)}^2$

$\Rightarrow (\frac{8}{4}{)}^2=(2{)}^2=4$