ExamBro
ExamBro
AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\begin{aligned} & \left(\cos 252^{\circ}-\sin 126^{\circ}\right)\left(\cos 252^{\circ}+\right. \\ & \left.\sin 126^{\circ}\right)\left(\sin ^2 126^{\circ}+\sin ^2 186^{\circ}+\sin ^2 66^{\circ}\right)=\end{aligned}\)

  1. A \(\frac{3 \sqrt{5}}{8}\)
  2. B \(\frac{-3 \sqrt{5}}{8}\)
  3. C \(\frac{-3 \sqrt{5}}{4}\)
  4. D \(\frac{3 \sqrt{5}}{4}\)
Verified Solution

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…