Test Index

KCET 2026 Mathematics Solved Paper

© examsnet.com

Question : 30 of 60

Marks: +1, -0

If

\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}

x^{2}

is equal to

$1-y^{2}$
$\sqrt{1-y^{2}}$
$-\sqrt{1-y^{2}}$
$1+y^{2}$

Solution:

Concept:

Use the identity

\sin^{-1} x + \sin^{-1} y = \frac{\pi}{2}

to express one angle in terms of the other, then apply trigonometric identities.

Explanation:

Let

\sin^{-1} x = A

and

\sin^{-1} y = B

.

Given,

A + B = \frac{\pi}{2}

.

So,

A = \frac{\pi}{2} - B

.

Since

x = \sin A

, we get

x = \sin\left(\frac{\pi}{2} - B\right)

.

Using

\sin\left(\frac{\pi}{2} - \theta\right) = \cos\theta

, we have

x = \cos B

.

Now,

y = \sin B

, so

\cos^2 B = 1 - \sin^2 B = 1 - y^2

.

Therefore,

x^2 = \cos^2 B = 1 - y^2

.

Answer:

The correct option is

1 - y^2

, i.e., Option A.

© examsnet.com

Go to Question:

Prev Question

Next Question