Advertisements
Advertisements
Question
Prove that:
Advertisements
Solution
\[LHS = 2\left( \sin \frac{5\pi}{12} \right) \left( \sin \frac{\pi}{12} \right)\]
\[ = \cos \left( \frac{5\pi}{12} - \frac{\pi}{12} \right) - \cos \left( \frac{5\pi}{12} + \frac{\pi}{12} \right) \left[ \because 2 \sin A \sin B = \cos (A - B) - \cos (A + B) \right]\]
\[ = \cos \frac{\pi}{3} - \cos \frac{\pi}{2}\]
\[ = \frac{1}{2} - 0\]
\[ = \frac{1}{2}\]
\[RHS = \frac{1}{2}\]
Hence, LHS = RHS
APPEARS IN
RELATED QUESTIONS
Show that :
Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that tan 20° tan 30° tan 40° tan 80° = 1.
Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
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 2x + cos 4x
Prove that:
sin 38° + sin 22° = sin 82°
Prove that:
sin 40° + sin 20° = cos 10°
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Prove that:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
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 \[xy + yz + zx = 0\]
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 \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
cos 40° + cos 80° + cos 160° + cos 240° =
cos 35° + cos 85° + cos 155° =
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 =
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Express the following as the product of sine and cosine.
cos 2θ – cos θ
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
Evaluate:
sin 50° – sin 70° + sin 10°
If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
