Question

The value of ${\sin }^2\alpha {\cos }^2\beta +{\cos }^2\alpha {\sin }^2\beta +{\sin }^2\alpha {\sin }^2\beta +{\cos }^2\alpha {\cos }^2\beta$ is

• A. $1$
• B. $0$
• C. $-1$
• D. $3$

Answer 1

The correct option is A $1$

$\Rightarrow ({\sin }^2\alpha {\cos }^2\beta +{\sin }^2\alpha {\sin }^2\beta )+({\cos }^2\alpha {\sin }^2\beta +{\cos }^2\alpha {\cos }^2\beta )={\sin }^2\alpha (co{s}^2\beta +{\sin }^2\beta )+co{s}^2\alpha (co{s}^2\beta +{\sin }^2\beta )={\sin }^2\alpha +co{s}^2\alpha =1$

Therefore, Answer is $1$