Question

If ${\sin }^2{\theta }_1+{\sin }^2{\theta }_2+{\sin }^2{\theta }_3=0$, then which of the following is NOT the possible value of ${\cos }^2{\theta }_1+{\cos }^2{\theta }_2+{\cos }^2{\theta }_3$.

• A. $3$
• B. $-3$
• C. $-1$
• D. $-2$

Answer 1

Answer: (B), (C), (D)

The correct options are
B $-3$
C $-1$
D $-2$

We have,
${\sin }^2{\theta }_1+{\sin }^2{\theta }_2+{\sin }^2{\theta }_3=0$
$\Rightarrow 1-{\cos }^2{\theta }_1+1-{\cos }^2{\theta }_2+1-{\cos }^2{\theta }_3=0,[\because {\sin }^{2}x+{\cos }^{2}x=1\forall x\in R]$
$\Rightarrow {\cos }^2{\theta }_1+{\cos }^2{\theta }_2+{\cos }^2{\theta }_3=3$
Hence option B,C,D are correct choices.