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COMEDK 2025 Evening Solved Paper

Question : 122 of 180

Marks: +1, -0

The value of

\frac{\sin ^2 20^{\circ}+\cos ^4 20^{\circ}}{\sin ^4 20^{\circ}+\cos ^2 20^{\circ}}

is :

Solution:

Concept:

Express

\sin^2 20^\circ

and

\cos^2 20^\circ

as variables using the identity

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

Explanation:

Let

s = \sin^2 20^\circ

and

c = \cos^2 20^\circ

Then

s + c = 1

and

c = 1 - s

The given expression becomes:

\frac{s + c^2}{s^2 + c}.

Substitute

c = 1 - s

into numerator and denominator:

Numerator:

s + (1 - s)^2 = s + 1 - 2s + s^2 = 1 - s + s^2

Denominator:

s^2 + (1 - s) = s^2 + 1 - s = 1 - s + s^2

Since numerator equals denominator, the fraction simplifies to

1

Answer:

The value is

1

(Option C).

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