Advertisements
Advertisements
Question
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
Advertisements
Solution
Given:
sin 2A = λ sin 2B
\[\Rightarrow \frac{\sin2A + \sin2B}{\sin2A - \sin2B} = \frac{\lambda + 1}{\lambda - 1}\]
\[ \Rightarrow \frac{2\sin\left( \frac{2A + 2B}{2} \right)\cos\left( \frac{2A - 2B}{2} \right)}{2\sin\left( \frac{2A - 2B}{2} \right)\cos\left( \frac{2A + 2B}{2} \right)} = \frac{\lambda + 1}{\lambda - 1} \left[ \because \sin A + \sin B = 2\sin\left( \frac{A + B}{2} \right)\cos\left( \frac{A - B}{2} \right) \text{and }\sin A - \sin B = 2\sin\left( \frac{A - B}{2} \right)\cos\left( \frac{A + B}{2} \right) \right]\]
\[ \Rightarrow \frac{\sin\left( A + B \right)\cos\left( A - B \right)}{\sin\left( A - B \right)\cos\left( A + B \right)} = \frac{\lambda + 1}{\lambda - 1}\]
\[ \Rightarrow \tan\left( A + B \right)\cot\left( A - B \right)=\frac{\lambda + 1}{\lambda - 1}\]
\[\Rightarrow\frac{\tan\left( A + B \right)}{\tan\left( A - B \right)}=\frac{\lambda + 1}{\lambda - 1}\]
APPEARS IN
RELATED QUESTIONS
Prove that:
Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
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 12x + sin 4x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
sin 40° + sin 20° = cos 10°
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
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 \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
If \[m \sin\theta = n \sin\left( \theta + 2\alpha \right)\], prove that \[\tan\left( \theta + \alpha \right) \cot\alpha = \frac{m + n}{m - n}\]
Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.
cos 35° + cos 85° + cos 155° =
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
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)]`
If secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.
