Question

The value of $3(sinx-cosx{)}^4+6(sinx+cosx{)}^2+4(si{n}^{6}x+co{s}^{6}x)=$

• A. $11$
• B. $12$
• C. $13$
• D. $14$

Answer 1

Answer: (C)

$3{\left(sinx-cosx\right)}^4+6{\left(sinx+cosx\right)}^2+4\left(si{n}^{6}x+co{s}^{6}x\right)$
$=3{\left(1-sin2x\right)}^2+6\left(1+sin2x\right)+4[{\left(si{n}^{2}x+co{s}^{2}x\right)}^3$
$-3si{n}^{2}xco{s}^{2}x\left(si{n}^{2}x+co{s}^{2}x\right)]$
$=3\left(1-2sin2x+si{n}^{2}2x\right)+6+6sin2x$
$+4\left[1-\frac{3}{4}si{n}^{2}2x\right]$
$=13+3si{n}^{2}2x-3si{n}^{2}2x=13$.