Question

$\frac{3-4{\sin }^2\theta }{{\cos }^2\theta }$ is equal to

• A. $3-{\cot }^2\theta$
• B. $3+{\cot }^2\theta$
• C. $3-{\tan }^2\theta$
• D. $3+{\tan }^2\theta$

Answer 1

The correct option is C $3-{\tan }^2\theta$

The given expression is

$\frac{3-4{\sin }^2\theta }{{\cos }^2\theta }=\frac{3\times 1-4{\sin }^2\theta }{{\cos }^2\theta }=\frac{3\times ({\sin }^2\theta +{\cos }^2\theta )-4{\sin }^2\theta }{{\cos }^2\theta }=\frac{3{\cos }^2\theta -{\sin }^2\theta }{{\cos }^2\theta }=3-\frac{{\sin }^2\theta }{{\cos }^2\theta }=3-{\tan }^2\theta .$