Question

What is the expression $({\sin }^{4}x-{\cos }^{4}x+1){\text{cosec}}^{2}x$ equal to?

• A. $1$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

The correct option is B $2$

$({\sin }^{4}x-{\cos }^{4}x+1){\text{cosec}}^{2}x$
$=\left[\right({\sin }^{2}x-{\cos }^{2}x\left)\right({\sin }^{2}x+{\cos }^{2}x)+1]{\text{cosec}}^{2}x$
$=({\sin }^{2}x-{\cos }^{2}x+1){\text{cosec}}^{2}x$
$=2{\sin }^{2}x{\text{cosec}}^{2}x=2$