Advertisements
Advertisements
प्रश्न
Prove that:
उत्तर
\[LHS = \cos \frac{\pi}{12} - \sin \frac{\pi}{12}\]
\[ = \cos \left( \frac{\pi}{2} - \frac{5\pi}{12} \right) - \sin \frac{\pi}{12}\]
\[ = \sin \left( \frac{5\pi}{12} \right) - \sin \frac{\pi}{12}\]
\[ = 2\sin \left( \frac{\frac{5\pi}{12} - \frac{\pi}{12}}{2} \right) \cos \left( \frac{\frac{5\pi}{12} + \frac{\pi}{12}}{2} \right) \left\{ \because \sin A - \sin B = 2\sin \left( \frac{A - B}{2} \right) \cos \left( \frac{A + B}{2} \right) \right\}\]
\[ = 2\sin \left( \frac{\pi}{6} \right) \cos \left( \frac{\pi}{4} \right)\]
\[ = 2 \times \frac{1}{2} \times \frac{1}{\sqrt{2}}\]
\[ = \frac{1}{\sqrt{2}}\]
Hence, LHS = RHS.
APPEARS IN
संबंधित प्रश्न
Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]
Prove that
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
Prove that:
sin 50° − sin 70° + sin 10° = 0
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
If cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ.
If \[m \sin\theta = n \sin\left( \theta + 2\alpha \right)\], prove that \[\tan\left( \theta + \alpha \right) \cot\alpha = \frac{m + n}{m - n}\]
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.
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
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.
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 cos 52° + cos 68° + cos 172° is
cos 35° + cos 85° + cos 155° =
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)
Express the following as the sum or difference of sine or cosine:
`cos (7"A")/3 sin (5"A")/3`
Express the following as the product of sine and cosine.
cos 2θ – cos θ
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`
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:
