The value of 4cos³ 40°-3cos 40° is : (a) (1)/(2) ( – Class 11 Business Mathematics Statistics | ConceptFirst

Question 33 of 36

4\cos^3 40°-3\cos 40°

(a)

\dfrac{1}{2}

(b)

\dfrac{\sqrt{3}}{2}

(c)

\dfrac{1}{\sqrt{2}}

(d)

-\dfrac{1}{2}

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Recognise the triple-angle identity $4\cos^3\theta-3\cos\theta=\cos 3\theta$ ; here it gives $\cos 120°=-\dfrac{1}{2}$ .

The multiple-angle formula for cosine is

$\cos 3\theta=4\cos^3\theta-3\cos\theta.$

With $\theta=40°$ :

$4\cos^3 40°-3\cos 40°=\cos(3\times 40°)=\cos 120°.$

…

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2025Set MARCH1 markMCQ
$4\cos^3 40°-3\cos 40°$
(a) $\dfrac{1}{2}$
(b) $\dfrac{\sqrt{3}}{2}$
(c) $\dfrac{1}{\sqrt{2}}$
(d) $-\dfrac{1}{2}$
›Reveal solutionSolution

Recognise the triple-angle identity $4\cos^3\theta-3\cos\theta=\cos 3\theta$ ; here it gives $\cos 120°=-\dfrac{1}{2}$ .

The multiple-angle formula for cosine is

$\cos 3\theta=4\cos^3\theta-3\cos\theta.$

With $\theta=40°$ :

$4\cos^3 40°-3\cos 40°=\cos(3\times 40°)=\cos 120°.$

…

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CBSE 2023Set MARCH1 markMCQ
$\sin 15^\circ \cos 15^\circ$
(a) $\dfrac{\sqrt{3}}{2}$
(b) $1$
(c) $\dfrac{1}{4}$
(d) $\dfrac{1}{2}$
›Reveal solutionSolution

$\sin15^\circ\cos15^\circ = \tfrac12\sin30^\circ = \tfrac12\cdot\tfrac12 = \tfrac14$ , so the answer is option (c).

Recall the double-angle formula

$\sin 2\theta = 2\sin\theta\cos\theta \;\Rightarrow\; \sin\theta\cos\theta = \frac{1}{2}\sin 2\theta.$

With $\theta = 15^\circ$ :

…

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CBSE 2020Set MARCH1 markMCQ
$\sin A + \cos A = 1$
(a) $\dfrac{1}{2}$
(b) $1$
(c) $2$
(d) $0$
›Reveal solutionSolution

Squaring $\sin A+\cos A=1$ and applying $\sin^2A+\cos^2A=1$ leaves $\sin 2A=0$ .

Given:

$\sin A + \cos A = 1.$

Square both sides:

$(\sin A + \cos A)^2 = 1^2$

$\sin^2 A + 2\sin A\cos A + \cos^2 A = 1.$

Use the Pythagorean identity $\sin^2 A + \cos^2 A = 1$ : …

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