Question

The value of $co{s}^4+\theta +si{n}^4\theta -6co{s}^2\theta si{n}^2\theta$ is

• A. $cos2\theta$
• B. $sin2\theta$
• C. $cos4\theta$
• D. none of these

Answer 1

The correct option is C

$cos4\theta$

$co{s}^4\theta +si{n}^4\theta -6co{s}^2\theta si{n}^2\theta =co{s}^4\theta +si{n}^4\theta -2co{s}^2\theta si{n}^2\theta -4co{s}^2\theta si{n}^2\theta =(co{s}^2\theta -si{n}^2\theta )-(2sin\theta cos\theta {)}^2=co{s}^{2}2\theta -si{n}^{2}2\theta =cos4\theta$