Question

${\cos }^4\theta -{\sin }^4\theta +1$is equal to :

• A. $2\cos e{c}^2\theta$
• B. $-2\cos e{c}^2\theta$
• C. $\frac{2}{{\tan }^2\theta }$
• D. $\frac{2{\cot }^2\theta }{\cos e{c}^2\theta }$

Answer 1

The correct option is D $\frac{2{\cot }^2\theta }{\cos e{c}^2\theta }$

$\cos \theta -{\sin }^4\theta +1$

$\Rightarrow ({\cos }^2\theta -{\sin }^2\theta )({\cos }^2\theta +{\sin }^2\theta )+1$

$\Rightarrow {\cos }^2\theta -{\sin }^2\theta +1$

$\Rightarrow {\cos }^2\theta +{\cos }^2\theta$

$\Rightarrow 2{\cos }^2\theta =\frac{2{\cos }^2\theta \times {\sin }^2\theta }{{\sin }^2\theta }=\frac{2{\cot }^2\theta }{{\csc }^2\theta }$