What is {p²}{q²} equal to? [NDA-I 2020]

Correct Answer is : (a−d)(c−a)(b−c)(d−b)(a-d)(c-a)/(b-c)(d-b)(b−c)(d−b)(a−d)(c−a)

Correct Answer is : (a−d)(c−a)(b−c)(d−b)(a-d)(c-a)/(b-c)(d-b)(b−c)(d−b)(a−d)(c−a)

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UPSC NDA I and II 2020 Math Solved Paper

DIRECTIONS (Qs. 16-18) : Read the following information and answer the three items 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

[NDA-I 2020]

Question : 18 of 120

Marks: +1, -0

What is

\frac{p^{2}}{q^{2}}

Solution: 👈: Video Solution

From,

p \cdot \tan x = q \cdot \tan y

p^{2} \cdot \tan^{2} x = q^{2} \cdot \tan^{2} y

\Rightarrow \frac{p^{2}}{q^{2}} = \frac{\tan^{2} y}{\tan^{2} x}

= \frac{(d-a)}{(b-d)} \cdot \frac{(a-c)}{(c-b)}

= \frac{(a-d)(c-a)}{(b-c)(d-b)}

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