Question

$si{n}^4\theta +2si{n}^2\theta (1-\frac{1}{cose{c}^2\theta })+co{s}^4\theta =$

• A. $1$
• B. $0$
• C. $1/2$
• D. $-1$

Answer 1

The correct option is A $1$

${\sin }^4\theta +2{\sin }^2\theta (1-\frac{1}{cose{c}^2\theta })+{\cos }^4\theta ={\sin }^4\theta +2{\sin }^2\theta (1-{\sin }^2\theta )+{\cos }^4\theta ={\sin }^4\theta +2{\sin }^2\theta {\cos }^2\theta +{\cos }^4\theta =({\sin }^2\theta +{\cos }^2\theta {)}^2=1$