Question

Period of $6{\cos }^{4}x-7{\sin }^{4}x$ is

• A. $\frac{\pi }{2}$
• B. $\pi$
• C. $\frac{3\pi }{2}$
• D. $2\pi$

Answer 1

Answer: (B)

$\pi$

Property of periodic function,
$f(x+T)=f\left(x\right)$
Let $f\left(x\right)=6co{s}^{4}x-7si{n}^{4}x$
assume $T=\pi /2$,
$6\left(cos\right(90+x){)}^4-7(sin(90+x){)}^4\ne 6co{s}^{4}x-7si{n}^{4}x$ (wrong assumption)
assume $T=\pi$,
$6\left(cos\right(\pi +x){)}^4-7(sin(\pi +x){)}^4=6co{s}^{4}x-7si{n}^{4}x$ (correct assumption)
So, period of $f\left(x\right)$ is $\pi$