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RRB Technician Grade I 13 March 2026 Paper

Question : 46 of 100

Marks: +1, -0

Simplify:

[{sin^{8}\theta -cos^{8}\theta }\frac{1}{sin^{4}\theta +cos^{4}\theta }]+2cos^{2}\theta

Solution:

Concept:

Use algebraic factorization and the Pythagorean identity

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

Explanation:

Factor the numerator using difference of squares:

\sin^8\theta - \cos^8\theta = (\sin^4\theta - \cos^4\theta)(\sin^4\theta + \cos^4\theta)

So the fraction simplifies to

\sin^4\theta - \cos^4\theta

Factor again:

\sin^4\theta - \cos^4\theta = (\sin^2\theta - \cos^2\theta)(\sin^2\theta + \cos^2\theta) = \sin^2\theta - \cos^2\theta

Now add the remaining term:

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

Using

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

, the final value is

1

Answer:

Option A:

1

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