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RRB NTPC Mains or Stage 2 Model Paper 3 with solutions

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Question : 38 of 120

Marks: +1, -0

I f

\cos A + \cos^2 A = 1

\sin^2 A + \sin^4 A

is equal to

1
$\frac{1}{2}$
0
– 1

Solution:

Concept:

Use the identity

\sin^2 A = 1-\cos^2 A

and the given equation to simplify the expression.

Explanation:

Given:

\cos A + \cos^2 A = 1

.

Rearrange:

\cos A = 1-\cos^2 A

.

Using

\sin^2 A = 1-\cos^2 A

, we get

\sin^2 A = \cos A

.

Square both sides:

\sin^4 A = \cos^2 A

.

Now add:

\sin^2 A + \sin^4 A = \cos A + \cos^2 A

.

From the given condition,

\cos A + \cos^2 A = 1

.

Therefore,

\sin^2 A + \sin^4 A = 1

.

Answer:

The value is

1

, so option A is correct.

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