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RRB Technician Grade 1 Model Paper 4

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Question : 46 of 100

Marks: +1, -0

\frac{sin^{4}\theta +cos^{4}\theta }{1-2sin^{2}\theta .cos^{2}\theta }=

________.

1
2
$-1$
0

Solution:

Concept:

Use the identity

\sin^2\theta + \cos^2\theta = 1

to simplify the numerator.

Explanation:

Rewrite

\sin^4\theta + \cos^4\theta

as

(\sin^2\theta + \cos^2\theta)^2 - 2\sin^2\theta\cos^2\theta

.

Since

\sin^2\theta + \cos^2\theta = 1

, the expression becomes

1 - 2\sin^2\theta\cos^2\theta

.

Substitute this into the given fraction:

\frac{\sin^4\theta + \cos^4\theta}{1 - 2\sin^2\theta\cos^2\theta} = \frac{1 - 2\sin^2\theta\cos^2\theta}{1 - 2\sin^2\theta\cos^2\theta}.

The numerator and denominator are identical, so the fraction equals

1

.

Answer:

1

(Option A).

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