Advertisements
Advertisements
प्रश्न
Prove that: \[\frac{\sin \left( A + B \right) + \sin \left( A - B \right)}{\cos \left( A + B \right) + \cos \left( A - B \right)} = \tan A\]
Advertisements
उत्तर
\[\text{ LHS }= \frac{\sin\left( A + B \right) + \sin\left( A - B \right)}{\cos\left( A + B \right) + \cos\left( A - B \right)}\]
\[ = \frac{\sin A \cos B + \cos A \sin B + \sin A \cos B - \cos A \sin B}{\cos A \cos B - \sin A \sin B + \cos A \cos B + \sin A \sin B}\]
\[ = \frac{2\sin A \cos B}{2\cos A \cos B}\]
\[ = \frac{\sin A}{\cos A}\]
\[ = \tan A\]
= RHS
Hence proved .
APPEARS IN
संबंधित प्रश्न
Find the value of: tan 15°
Prove the following: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`
Prove the following:
`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
`(sin x - sin 3x)/(sin^2 x - cos^2 x) = 2sin x`
Prove the following:
`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`
Prove the following:
`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`
Prove that: `((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos 7x + cos 5x) + (cos 9x + cos 3x)) = tan 6x`
If \[\sin A = \frac{1}{2}, \cos B = \frac{12}{13}\], where \[\frac{\pi}{2}\]< A < π and \[\frac{3\pi}{2}\] < B < 2π, find tan (A − B).
Evaluate the following:
sin 78° cos 18° − cos 78° sin 18°
Prove that
Prove that:
Prove that:
\[\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}\]
Prove that:
\[\frac{\sin \left( A - B \right)}{\cos A \cos B} + \frac{\sin \left( B - C \right)}{\cos B \cos C} + \frac{\sin \left( C - A \right)}{\cos C \cos A} = 0\]
Prove that:
Prove that:
\[\frac{\tan^2 2x - \tan^2 x}{1 - \tan^2 2x \tan^2 x} = \tan 3x \tan x\]
If sin α + sin β = a and cos α + cos β = b, show that
If sin α sin β − cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.
If tan α = x +1, tan β = x − 1, show that 2 cot (α − β) = x2.
Find the maximum and minimum values of each of the following trigonometrical expression:
sin x − cos x + 1
If α + β − γ = π and sin2 α +sin2 β − sin2 γ = λ sin α sin β cos γ, then write the value of λ.
Write the maximum and minimum values of 3 cos x + 4 sin x + 5.
If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to
If in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =
If \[\cos P = \frac{1}{7}\text{ and }\cos Q = \frac{13}{14}\], where P and Q both are acute angles. Then, the value of P − Q is
If cot (α + β) = 0, sin (α + 2β) is equal to
If α and β are the solutions of the equation a tan θ + b sec θ = c, then show that tan (α + β) = `(2ac)/(a^2 - c^2)`.
If cos(θ + Φ) = m cos(θ – Φ), then prove that 1 tan θ = `(1 - m)/(1 + m) cot phi`
[Hint: Express `(cos(theta + Φ))/(cos(theta - Φ)) = m/1` and apply Componendo and Dividendo]
The value of sin(45° + θ) - cos(45° - θ) is ______.
If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.
If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.
If tanθ = `a/b`, then bcos2θ + asin2θ is equal to ______.
3(sinx – cosx)4 + 6(sinx + cosx)2 + 4(sin6x + cos6x) = ______.
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
State whether the statement is True or False? Also give justification.
If tanθ + tan2θ + `sqrt(3)` tanθ tan2θ = `sqrt(3)`, then θ = `("n"pi)/3 + pi/9`
