Question

If $0^{\circ }<\theta <{90}^{\circ }and{\cos }^2\theta -{\sin }^2\theta =\frac{1}{2}$ then what is the value of $\theta$?

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (A)

${30}^{\circ }$

${\cos }^2\theta -{\sin }^2\theta =\frac{1}{2}\Rightarrow 1-2{\sin }^2\theta =\frac{1}{2}\Rightarrow 2{\sin }^2\theta =\frac{1}{2}\Rightarrow {\sin }^2\theta =\frac{1}{4}\Rightarrow \sin \theta =\frac{1}{2}=\sin {30}^0\Rightarrow \theta =30$