4 ( 3 + ) ( 3 - )= - Vidyadip

MCQ

$4 \sin \left(\frac{\pi}{3}+\theta\right) \sin \left(\frac{\pi}{3}-\theta\right)=$

A
$1+\cos 2 \theta$
B
$1-2 \cos 2 \theta$
C
$2 \cos 2 \theta-1$
✓
$1+2 \cos 2 \theta$

✓

Answer

Correct option: D.

$1+2 \cos 2 \theta$

(D)
$4 \sin \left(\frac{\pi}{3}+\theta\right) \sin \left(\frac{\pi}{3}-\theta\right)$
$=2\left[2 \sin \left(\frac{\pi}{3}+\theta\right) \sin \left(\frac{\pi}{3}-\theta\right)\right]$
$=2\left[\cos \left(\frac{\pi}{3}+\theta-\frac{\pi}{3}+\theta\right)-\cos \left(\frac{\pi}{3}+\theta+\frac{\pi}{3}-\theta\right)\right]$
$=2 [\cos 2 \theta-\cos \left(\frac{2 \pi}{3}\right)]$
$=2 \cos 2 \theta+1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

A circle touches the Y-axis at the point (0, 4) and cuts the X-axis in a chord of length 6 units. The radius of the circle is

${^\text{5}}\text{C}_{\text{1}}+{^\text{5}}\text{C}_{\text{2}}+{^\text{5}}\text{C}_{\text{3}}+{^\text{5}}\text{C}_{\text{4}}+{^\text{5}}\text{C}_{\text{5}}$is equal to :

The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is

The equation of the line passing through the point of intersection of the lines 2x + y - 4 = 0 , x - 3y + 5 = 0 and lying at a distance of $\sqrt{5}$ units from the origin, is

If a and b are two arbitrary constants, then the straight line (a-2b)x + (a+3b)y + 3a+ 4b = 0 will pass through

If the lines $y= m _1 x+ c _1, y= m _2 x+ c _2$ and $y=m_3 x+c_3$, are concurrent, then

If $\arg z<0$, then $\arg (-z)-\arg (z)$ is equal to

The value of a for which the system of equations $a^3 x+(a+1) y+(a+2)^3 z=0$, $a x+(a+$ 1)y + (a + 2)z = 0 and x + y + z = 0 has a non zero solution is

If $\lim _{x \rightarrow \infty}\left[\frac{x^3+1}{x^2+1}-(a x+b)\right]=2$, then

A line L makes intercepts a and b on the coordinate axes. The axes are rotated through an angle \[ \theta\] in the positive direction, keeping the origin fixed. If the line L makes intercepts p and q on the new coordinate axes, then $\frac{1}{a^2}+\frac{1}{b^2}=$