Question

The given relation $si{n}^{2}Aco{s}^{2}B+co{s}^{2}Asi{n}^{2}B+co{s}^{2}Aco{s}^{2}B+si{n}^{2}Asi{n}^{2}B=2$ is

• A. True
• B. False

Answer 1

The correct option is B False

As we know that

${\sin }^2\theta +{\cos }^2\theta =1$

${\sin }^{2}A{\cos }^{2}B+{\cos }^{2}A{\sin }^{2}B+{\cos }^{2}A{\cos }^{2}B+{\sin }^{2}A{\sin }^{2}B={\sin }^{2}A({\cos }^{2}A+{\sin }^{2}B)+{\cos }^{2}A({\sin }^{2}B+{\cos }^{2}B)$

$={\sin }^{2}A\left(1\right)+{\cos }^{2}A\left(1\right)$

$={\sin }^{2}A+{\cos }^{2}A$

$=1$

So the given relation is $\text{False}$