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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2020 · Mathematics · Trigonometric Ratios & Identities

Paragraph: Read the following information and answer that follow:...

Paragraph: Read the following information and answer that follow: Let asin⁡2x+bcos⁡2x=c;bsin⁡2y+acos⁡2y=da \sin ^2 x+b \cos ^2 x=c ; b \sin ^2 y+a \cos ^2 y=d and ptan⁡x=qtan⁡yp \tan x=q \tan y.
Question: What is d−ab−d\frac{d-a}{b-d} equal to?

Options

  1. Asin⁡2y\sin ^2 y
  2. Bcos⁡2y\cos ^2 y
  3. Ctan⁡2y\tan ^2 y
  4. Dcot⁡2y\cot ^2 y

Correct answer

C. tan⁡2y\tan ^2 y

Step-by-step solution

From bsin⁡2y+acos⁡2y=db \sin ^2 y+a \cos ^2 y=dbsin⁡2y+acos⁡2y=d(sin⁡2y+cos⁡2y)(b−d)sin⁡2y=(d−a)cos⁡2y⇒sin⁡2ycos⁡2y=(d−a)(b−d)⇒tan⁡2y=(d−a)(b−d)\begin{aligned} & b \sin ^2 y+a \cos ^2 y=d\left(\sin ^2 y+\cos ^2 y\right) \\ & (b-d) \sin ^2 y=(d-a) \cos ^2 y \\ & \Rightarrow \frac{\sin ^2 y}{\cos ^2 y}=\frac{(d-a)}{(b-d)} \Rightarrow \tan ^2 y=\frac{(d-a)}{(b-d)} \end{aligned}$$
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