Question

Let $x=(1+\sin A)(1-\sin B)(1+\sin C),y=(1-\sin A)(1-\sin B)(1-\sin C)$ and if $x=y$, then

• A. $x=\cos A\cos B\cos C$
• B. $y=\sin A\sin B\sin C$
• C. $y=-\cos A\cos B\cos C$
• D. $x=-\sin A\sin B\sin C$

Answer 1

Answer: (A), (C)

$x=\cos A\cos B\cos C$
$y=-\cos A\cos B\cos C$

$P=(1+\sin A)(1+\sin B)(1+\sin C)=(1-\sin A)(1-\sin B)(1-\sin C)$......As $x=y$ (given)
$\Rightarrow P^2=(1+\sin A)(1+\sin B)(1+\sin C)\times (1-\sin A)(1-\sin B)(1-\sin C)$
$\Rightarrow P^2=(1-{\sin }^{2}A)(1-{\sin }^{2}B)(1-{\sin }^{2}C)={\cos }^{2}A{\cos }^{2}B{\cos }^{2}C$
$\therefore P=\pm \cos A\cos B\cos C$