Question

Assertion :The equation ${\sin }^{2}x+{\cos }^{2}y=2{\sec }^{2}z$ is only solvable when $|\sin x|=1,|\cos y|=1$ and $|\sin z|=1$, where $x,y,z\in R$ because Reason: Maximum value of $|\sin x|$ and $|\cos y|$ is $1$ and minimum value of $|\sec z|$ is $1$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect and Reason is incorrect

Answer 1

The correct option is D Assertion is incorrect and Reason is incorrect

Maximum value of L.H.S of assertion is 2. and the minimum value of R.H.S is 2
and this will happen only if ${\sin }^{2}x$ and ${\cos }^{2}y$ attains its maximum value and ${\sec }^{2}z$ attains its minimum value
i.e $\sin x=\pm 1,\cos y=\pm 1$ and $\sec z=\pm 1$
So assertion is incorrect and reason is also incorrect.