What is d-a/b-d equal to?

Correct Answer is : tan⁡2y²ytan2y

Correct Answer is : tan⁡2y²ytan2y

Test Index

UPSC NDA I and II 2020 Math Solved Paper

Question Numbers: 46-48

Direction: 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

Question : 47 of 120

Marks: +1, -0

What is

\frac{d-a}{b-d}

equal to?

Solution:

Concept:

The trigonometric identity

1+\tan^2 y = \sec^2 y

is used to transform the given equation.

Explanation:

Start with

b\sin^2 y + a\cos^2 y = d

Divide every term by

\cos^2 y

to get

b\tan^2 y + a = d\sec^2 y

Replace

\sec^2 y

1+\tan^2 y

using the identity:

b\tan^2 y + a = d(1+\tan^2 y)

Expand the right side:

b\tan^2 y + a = d + d\tan^2 y

Bring all terms containing

\tan^2 y

to the left and constants to the right:

b\tan^2 y - d\tan^2 y = d - a

Factor

\tan^2 y

\tan^2 y (b-d) = d-a

Since

b \neq d

, divide both sides by

b-d

to isolate

\tan^2 y

\tan^2 y = \frac{d-a}{b-d}

Thus the expression

\frac{d-a}{b-d}

equals

\tan^2 y

Answer:

Option C:

\tan^{2}y

Go to Question:

Prev Question

Next Question