Advertisements
Advertisements
प्रश्न
Prove that:
Advertisements
उत्तर
\[LHS = 2\left( \sin \frac{5\pi}{12} \right) \left( \cos \frac{\pi}{12} \right)\]
\[ = \sin \left( \frac{5\pi}{12} + \frac{\pi}{12} \right) + \sin \left( \frac{5\pi}{12} - \frac{\pi}{12} \right) \left[ \because 2 \sin A \cos B = \sin (A + B) + \sin (A - B) \right]\]
\[ = \sin \frac{\pi}{2} + \sin \frac{\pi}{3}\]
\[ = 1 + \frac{\sqrt{3}}{2}\]
\[ = \frac{2 + \sqrt{3}}{2}\]
\[RHS = \frac{2 + \sqrt{3}}{2}\]
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]
Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
Express each of the following as the product of sines and cosines:
cos 12x + cos 8x
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
Prove that:
sin 47° + cos 77° = cos 17°
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
Prove that:
Prove that:
Prove that:
If cosec A + sec A = cosec B + sec B, prove that tan A tan B = \[\cot\frac{A + B}{2}\].
If cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 0.
If \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
If (cos α + cos β)2 + (sin α + sin β)2 = \[\lambda \cos^2 \left( \frac{\alpha - \beta}{2} \right)\], write the value of λ.
If sin A + sin B = α and cos A + cos B = β, then write the value of tan \[\left( \frac{A + B}{2} \right)\].
Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), then write the value of tan A tan B tan C.
cos 40° + cos 80° + cos 160° + cos 240° =
If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos2 (θ − ϕ) =
The value of sin 50° − sin 70° + sin 10° is equal to
If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =
Express the following as the product of sine and cosine.
sin A + sin 2A
Express the following as the product of sine and cosine.
cos 2A + cos 4A
Prove that:
cos 20° cos 40° cos 80° = `1/8`
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:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Evaluate-
cos 20° + cos 100° + cos 140°
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
