The value of ≤ft(π/5) is ...

Correct Answer is : 1+54{1+{5}}{4}41+5

Correct Answer is : 1+54{1+{5}}{4}41+5

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MHTCET 19 Apr 2026 Shift 1 Paper

Question : 104 of 150

Marks: +1, -0

The value of

\cos \left(\frac{\pi}{5}\right)

is ...

Solution:

Concept:

Use the relation

\cos 108^\circ = -\cos 72^\circ

and standard multiple-angle formulas to find

\cos 36^\circ

Explanation:

Let

\theta = \frac{\pi}{5} = 36^\circ

Then

3\theta = 108^\circ

and

2\theta = 72^\circ

Since

\cos 108^\circ = -\cos 72^\circ

, we get:

\cos 3\theta = -\cos 2\theta.

Let

x = \cos \theta

Use

\cos 3\theta = 4x^3 - 3x

and

\cos 2\theta = 2x^2 - 1

So:

4x^3 - 3x = -(2x^2 - 1).

Simplify to get:

4x^3 + 2x^2 - 3x - 1 = 0.

Factorising:

(x+1)(4x^2 - 2x - 1) = 0.

Thus,

x = -1

x = \frac{1 \pm \sqrt{5}}{4}

Since

\cos 36^\circ

is positive, we discard negative values:

x = \frac{1 + \sqrt{5}}{4}.

Answer:

\cos \left(\frac{\pi}{5}\right) = \frac{1+\sqrt{5}}{4}

Hence, the correct option is Option C.

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