AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\begin{aligned} & \left(\cos 252^{\circ}-\sin 126^{\circ}\right)\left(\cos 252^{\circ}+\right. \\ & \left.\sin 126^{\circ}\right)\left(\sin ^2 126^{\circ}+\sin ^2 186^{\circ}+\sin ^2 66^{\circ}\right)=\end{aligned}\)
- A \(\frac{3 \sqrt{5}}{8}\)
- B \(\frac{-3 \sqrt{5}}{8}\)
- C \(\frac{-3 \sqrt{5}}{4}\)
- D \(\frac{3 \sqrt{5}}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{-3 \sqrt{5}}{8}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(\cos 252^{\circ}-\sin 126^{\circ}\right)\left(\cos 252^{\circ}+\sin 126^{\circ}\right) \\ & \left(\sin ^2 126^{\circ}+\sin ^2 186^{\circ}+\sin ^2 66^{\circ}\right) \\ & =\left(\cos ^2 252^{\circ}-\sin ^2 126^{\circ}\right)\left(\sin ^2 126^{\circ}+\sin ^2…
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