Question

$(ta{n}^2\theta +co{s}^2\theta +2tan\theta cos\theta )$ simplifies to

• A. $si{n}^2\theta \cdot co{s}^2\theta +1$
• B. $se{c}^2\theta \cdot cose{c}^2\theta$
• C. $si{n}^2\theta -cose{c}^2\theta$
• D. None

Answer 1

Answer: (B)

$se{c}^2\theta \cdot cose{c}^2\theta$

$ta{n}^2\theta +co{s}^2\theta +2tan\theta \cdot cos\theta$
$=(tan\theta +cos\theta {)}^2$
$=(\frac{sin\theta }{cos\theta }+\frac{cos\theta }{sin\theta })$
$=\left(\frac{1}{sin\theta cos\theta }\right)=se{c}^2\theta \cdot cose{c}^2\theta$