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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

What is the value of the following? ( 24^ ^ + 66^ ^ )( 24^ ^ - 66^...

What is the value of the following? (sin⁡24∘+cos⁡66∘)(sin⁡24∘−cos⁡66∘)\left(\sin 24^{{}^{\circ}}+\cos 66^{{}^{\circ}}\right)\left(\sin 24^{{}^{\circ}}-\cos 66^{{}^{\circ}}\right)

Options

  1. A−1-1
  2. B00
  3. C11
  4. D22

Correct answer

B. 00

Step-by-step solution

(sin⁡24∘+cos⁡66∘)(sin⁡24∘−cos⁡66∘)=sin⁡224∘−cos⁡266∘\begin{aligned} & \left(\sin 24^{{}^{\circ}}+\cos 66^{{}^{\circ}}\right)\left(\sin 24^{{}^{\circ}}-\cos 66^{{}^{\circ}}\right) \\ & =\sin ^2 24^{{}^{\circ}}-\cos ^2 66^{{}^{\circ}}\end{aligned}=sin⁡224∘−cos⁡2(90∘−24∘)=sin⁡224∘−sin⁡224∘=0\begin{aligned} & =\sin ^2 24^{{}^{\circ}}-\cos ^2\left(90^{{}^{\circ}}-24^{{}^{\circ}}\right) \\ & =\sin ^2 24^{{}^{\circ}}-\sin ^2 24^{{}^{\circ}}=0\end{aligned}$
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