Question

If $({\cos }^{2}x+\frac{1}{{\cos }^{2}x})(1+{\tan }^{2}2y)(3+\sin 3z)=4,$then

• A. $x$ may be a multiple of $\pi$
• B. $x$ can not be an even multiple of $\pi$
• C. $z$ can be a multiple of $\pi$
• D. $y$ can be a multiple of $\pi /2$

Answer 1

The correct option is D $y$ can be a multiple of $\pi /2$

$minvalueof(co{s}^{2}x+(\frac{1}{co{s}^{2}x}\left)\right)=2minvalueof1+ta{n}^{2}2y=1andminvalueof3+sin3z=3-1=2Hencexmaybeamultipleof\pi becauseminimumvaluewilloccuronlywhenco{s}^{2}x=\left(\frac{1}{co{s}^{2}x}\right)=1ycanbemultipleof\left(\frac{\pi }{2}\right)suchthattan\left(2y\right)=0$