CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Circular Measurement of Angle

Prove that si...

Question

Prove that $(sin 3 x + sin x) sin x + (cos 3 x - cos x) cos x = 0$

Open in App

Solution

$L . H . S = (sin 3 x + sin x) sin x + (cos 3 x - cos x) cos x$
$= [2 sin (\frac{3 x + x}{2}) cos (\frac{3 x - x}{2})] sin x + [- 2 sin (\frac{3 x + x}{2}) sin (\frac{3 x - x}{2})] cos x$
$= [2 sin 2 x cos x] sin x + [- 2 sin 2 x sin x] cos x$
$= sin 2 x (2 sin x cos x) - sin 2 x (2 sin x cos x)$
$= sin 2 x \cdot sin 2 x - sin 2 x \cdot sin 2 x$
$= 0 = R . H . S$

Hence proved.

Suggest Corrections

thumbs-up

0

Similar questions

(sin 3 x + sin x) sin x + (cos 3 x - cos x) cos x = 0

Q. The number of solutions of the equation

(sin 3 x + sin x) sin x + (cos 3 x - cos x) cos x = 0

[- π, π]

\frac{c o s 4 x + c o s 3 x + c o s 2 x}{s i n 4 x + s i n 3 x + s i n 2 x} = c o t 3 x

sin 3 x + sin 2 x - sin x = 4 sin x cos \frac{x}{2}, cos \frac{3 x}{2}

\frac{{cos}^{3} x - {sin}^{3} x}{cos x - sin x} = \frac{1}{2} (2 + sin 2 x)

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Circular Measurement of Angle

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon