Question

$Ifsinx+si{n}^{2}x+si{n}^{3}x=1,thenco{s}^{6}x-4co{s}^{4}x+8co{s}^{2}xisequalto$

• A. 0
• B. 2
• C. 4
• D. 8

Answer 1

The correct option is C

4

sin x(1 + $si{n}^2$ x) = 1 - $si{n}^2$ x = $co{s}^2$ x

sin x(2 - $co{s}^2$ x) = $co{s}^2$ x $\Rightarrow$ $si{n}^2$ x$(2-co{s}^{2}x{)}^2$ = $co{s}^4$ x [squaring both sides]

$\Rightarrow$(1 - $co{s}^2$ x) (4 - 4 $co{s}^2$ x + $co{s}^2$x) = $co{s}^4$x

$\Rightarrow$ $co{s}^{6}x-4co{s}^{4}x+8$ $co{s}^2$ x = 4