Question

Assertion :Statement 1 The equation ${\sin }^{2}x+{\cos }^{2}y=2{\sec }^{2}z$ is solvable when only $\sin x=1;\cos y=1$ and $\sec z=1$ where
$x,y,zϵR.$ Reason: The maximum value of sin x and cos y is 1 and the minimum value of sec z is 1

• A. if both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
• B. if both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. if STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. if STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is A if both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1

Max of ${\sin }^{2}x=1$ and ${\cos }^{2}y=1$

Min of ${\sec }^{2}z=1$

Therefore solution exits only at $x=y=z=1$

As $-1\le (\sin x,\cos x)\le 1,\sec x\in (-\infty ,-1)\cup (1,\infty )$