Paragraph: Read the following information and answer that follow: Let a ^2 x+b ^2 x=c ; b ^2 y+a ^2 y=d and p x=q y . Question: What is ^2 x equal to ?

Correct answer: A. (c-b)/(a-c) aligned & From a ^2 x+b ^2 x=c & a ^2 x+b ^2 x=c( ^2 x+ ^2 x) & (a-c) ^2 x=(c-b) ^2 x & ( ^2 x)/( ^2 x)=((c-b))/((a-c)) & ^2 x=((c-b))/((a-c)) aligned

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

a \sin ^2 x+b \cos ^2 x=c ; b \sin ^2 y+a \cos ^2 y=d

and

p \tan x=q \tan y

.
Question: What is

\tan ^2 x

equal to ?

Options

A $\frac{c-b}{a-c}$
B $\frac{a-c}{c-b}$
C $\frac{c-a}{c-b}$
D $\frac{c-b}{c-a}$

Correct answer

A. $\frac{c-b}{a-c}$

Step-by-step solution

\begin{aligned} & \text{\text{ From } } a \sin ^2 x+b \cos ^2 x=c \\ & a \sin ^2 x+b \cos ^2 x=c\left(\sin ^2 x+\cos ^2 x\right) \\ & (a-c) \sin ^2 x=(c-b) \cos ^2 x \\ & \Rightarrow \frac{\sin ^2 x}{\cos ^2 x}=\frac{(c-b)}{(a-c)} \\ & \Rightarrow \tan ^2 x=\frac{(c-b)}{(a-c)} \end{aligned}

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