Advertisements
Advertisements
प्रश्न
Prove that: (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0
उत्तर
L.H.S. = (sin 3x + sin x) sin x + (cos 3x – cos x) cosx
= sin 3x sin x + sin2x + cos 3x cos x – cos2x
= (cos 3x cos x + sin 3x sin x) – (cos2 x – sin2x)
= cos (3x - x) - cos 2x
= cos 2x – cos 2x
= 0 [∵ cos (A – B) = cos A cos B + sin A sin B]
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the values of other five trigonometric functions if `sin x = 3/5` x lies in second quadrant.
Find the values of other five trigonometric functions if ` tan x = - 5/12`, x lies in second quadrant.
Find the value of the trigonometric function sin 765°.
Find the value of the trigonometric function cosec (–1410°).
Find the value of the trigonometric function tan `(19pi)/3`.
Find the value of the trigonometric function sin `(-11pi)/3`.
Find the value of the trigonometric function cot `(-( 15pi)/4)`.
Find the value of the other five trigonometric functions
Find the value of the other five trigonometric functions
Find the value of the other five trigonometric functions
\[\tan x = \frac{3}{4},\] x in quadrant III
Find the value of the other five trigonometric functions
\[\sin x = \frac{3}{5},\] x in quadrant I
If sin \[x = \frac{12}{13}\] and x lies in the second quadrant, find the value of sec x + tan x.
If sin\[x = \frac{3}{5}, \tan y = \frac{1}{2}\text{ and }\frac{\pi}{2} < x < \pi < y < \frac{3\pi}{2},\] find the value of 8 tan \[x - \sqrt{5} \sec y\]
If sin x + cos x = 0 and x lies in the fourth quadrant, find sin x and cos x.
If \[\cos x = - \frac{3}{5}\text{ and }\pi < x < \frac{3\pi}{2}\] find the values of other five trigonometric functions and hence evaluate \[\frac{cosec x + \cot x}{\sec x - \tan x}\]
Find the value of the following trigonometric ratio:
Find the value of the following trigonometric ratio:
sin 17π
Find the value of the following trigonometric ratio:
\[\tan\frac{11\pi}{6}\]
Find the value of the following trigonometric ratio:
Find the value of the following trigonometric ratio:
\[\tan \frac{7\pi}{4}\]
