Advertisements
Advertisements
प्रश्न
Prove that:
Advertisements
उत्तर
Consider LHS:
\[\cos \left( \frac{\pi}{4} + x \right) + \cos\left( \frac{\pi}{4} - x \right)\]
\[ = 2\cos \left\{ \frac{\left( \frac{\pi}{4} + x \right) + \left( \frac{\pi}{4} - x \right)}{2} \right\}\cos \left\{ \frac{\left( \frac{\pi}{4} + x \right) - \left( \frac{\pi}{4} + x \right)}{2} \right\} \left\{ \because \cos A + \cos B = 2\cos \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[= 2\cos \left\{ \frac{\frac{\pi}{4} + x + \frac{\pi}{4} - x}{2} \right\}\cos \left\{ \frac{\frac{\pi}{4} + x - \frac{\pi}{4} + x}{2} \right\}\]
\[ = 2\cos$\left( \frac{\pi}{4} \right)$ \cos x\]
\[ = 2 \times \frac{1}{\sqrt{2}} \times \cos x\]
\[ = \sqrt{2}\cos x\]
= RHS
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
Express each of the following as the product of sines and cosines:
sin 5x − sin x
Prove that:
sin 38° + sin 22° = sin 82°
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
If \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), then write the value of tan A tan B tan C.
The value of sin 50° − sin 70° + sin 10° is equal to
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =
If \[\tan\alpha = \frac{x}{x + 1}\] and
Express the following as the sum or difference of sine or cosine:
cos(60° + A) sin(120° + A)
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
If sin(y + z – x), sin(z + x – y), sin(x + y – z) are in A.P, then prove that tan x, tan y and tan z are in A.P.
If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
