Question

If $(1+\sin x)(1+\sin y)(1+\sin z)=(1-\sin x)(1-\sin y)(1-\sin z)=k$ then k has the value

• A. $\pm \cos x\cos y\cos z$
• B. $\pm \sin x\sin y\sin z$
• C. $\pm 3\sin x\sin y\sin z$
• D. None of these

Answer 1

The correct option is A $\pm \cos x\cos y\cos z$

Multiply both sides by $(1+\sin x)(1+\sin y)(1+\sin z)$
$\Rightarrow (1+\sin x)(1+\sin y)(1+\sin z)$
$=(1-{\sin }^{2}x)(1-{\sin }^{2}y)(1-{\sin }^{2}z)$
$=\cos 2x\cos 2y\cos 2z$
$\Rightarrow (1+\sin x)(1+\sin y)(1+\sin z)$
$=\pm \cos x\cos y\cos z$