Advertisements
Advertisements
प्रश्न
Express the following as the product of sine and cosine.
sin A + sin 2A
बेरीज
Advertisements
उत्तर
sin A + sin 2A = 2 sin`(("A + 2A")/2) cos (("A - 2A")/2)` ...`[∵ sin "C" + sin "D" = sin (("C + D")/2) cos (("C - D")/2)]`
= 2 sin `"3A"/2` cos `"A"/2` ...[∵ cos(-θ) = cos θ]
shaalaa.com
Transformation Formulae
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
sin 40° + sin 20° = cos 10°
Prove that \[\cos x \cos \frac{x}{2} - \cos 3x \cos\frac{9x}{2} = \sin 7x \sin 8x\]
Prove that:
\[\frac{\sin A - \sin B}{\cos A + \cos B} = \tan\frac{A - B}{2}\]
Prove that:
\[\frac{\cos 3A + 2 \cos 5A + \cos 7A}{\cos A + 2 \cos 3A + \cos 5A} = \frac{\cos 5A}{\cos 3A}\]
Prove that:
\[\frac{\sin 3A + \sin 5A + \sin 7A + \sin 9A}{\cos 3A + \cos 5A + \cos 7A + \cos 9A} = \tan 6A\]
Prove that:
\[\frac{\sin 5A - \sin 7A + \sin 8A - \sin 4A}{\cos 4A + \cos 7A - \cos 5A - \cos 8A} = \cot 6A\]
Prove that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
Evaluate-
cos 20° + cos 100° + cos 140°
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.
