Advertisements
Advertisements
प्रश्न
Prove that:
उत्तर
Consider LHS:
\[ \frac{\cos 3A + 2\cos 5A + \cos 7A}{\cos A + 2\cos 3A + \cos 5A}\]
\[ = \frac{\cos 3A + \cos 7A + 2\cos 5A}{\cos A + \cos 5A + 2\cos 3A}\]
\[ = \frac{2\cos \left( \frac{3A + 7A}{2} \right) \cos \left( \frac{3A - 7A}{2} \right) + 2\cos 5A}{2\cos \left( \frac{A + 5A}{2} \right) \cos \left( \frac{A - 5A}{2} \right) + 2\cos 3A}\]
\[ \]
\[ = \frac{2\cos 5A \cos \left( - 2A \right) + 2\cos 5A}{2\cos 3A \cos \left( - 2A \right) + 2\cos 3A}\]
\[ = \frac{2\cos 5A \cos 2A + 2\cos 5A}{2\cos 3A \cos 2A + 2\cos 3A}\]
\[ = \frac{2\cos 5A \left[ \cos 2A + 1 \right]}{2\cos 3A \left[ \cos 2A + 1 \right]}\]
\[ = \frac{\cos 5A}{\cos 3A}\]
= RHS
Hence, RHS = LHS.
APPEARS IN
संबंधित प्रश्न
Prove 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 40° tan 60° tan 80° = 3
Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
Prove that
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
Prove that:
sin 38° + sin 22° = sin 82°
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Prove that:
Prove that:
Prove that:
Prove that:
If \[m \sin\theta = n \sin\left( \theta + 2\alpha \right)\], prove that \[\tan\left( \theta + \alpha \right) \cot\alpha = \frac{m + n}{m - n}\]
Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]
If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].
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° =
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
sin 47° + sin 61° − sin 11° − sin 25° is equal to
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
If \[\tan\alpha = \frac{x}{x + 1}\] and
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:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
Evaluate-
cos 20° + cos 100° + cos 140°
Evaluate:
sin 50° – sin 70° + sin 10°
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.
Find the value of tan22°30′. `["Hint:" "Let" θ = 45°, "use" tan theta/2 = (sin theta/2)/(cos theta/2) = (2sin theta/2 cos theta/2)/(2cos^2 theta/2) = sintheta/(1 + costheta)]`
