Question

If sinx + $si{n}^{2}x$ = 1 Then the value of $co{s}^{12}x+3co{s}^{10}x+3co{s}^{8}x+co{s}^{6}x$ is equal to

• A. 1
• B. -1
• C. 2
• D. -2

Answer 1

The correct option is A

1

$co{s}^{12}x+3co{s}^{10}x+3co{s}^{8}x+co{s}^{6}x=co{s}^{6}x[co{s}^{6}x+3co{s}^{4}x+3co{s}^{2}x+1]=co{s}^{6}x(co{s}^{2}x+1{)}^3=[co{s}^{2}x(co{s}^{2}x+1){]}^3=[co{s}^{2}x+co{s}^{2}x{]}^3=[si{n}^{2}x+sinx{]}^3=1^3=1$