Advertisements
Advertisements
प्रश्न
Prove the following:
`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`
उत्तर
L.H.S. = cos `((3x)/4 + x) - cos ( (3x) /4 - x)`
= - 2sin `[((3x)/4 + x) /2+ ( (3x) /4 - x)/2] sin [((3pi)/4)/2- ((3pi)/4-x)/2]`
[cos (a + b) - cos (a - b) = - 2sin `((a +b)/2) sin ((a + b )/2)`
= - 2sin `((3pi)/4) sin x = - 2 (pi - pi/4) sin x`
= - 2 x `1/sqrt2 sin x = - sqrt2 sin x` = R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the value of: tan 15°
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`
If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
sin (A − B)
If \[\sin A = \frac{12}{13}\text{ and } \sin B = \frac{4}{5}\], where \[\frac{\pi}{2}\] < A < π and 0 < B < \[\frac{\pi}{2}\], find the following:
cos (A + B)
Prove that
Prove that
Prove that:
sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.
Prove that: \[\frac{\sin \left( A + B \right) + \sin \left( A - B \right)}{\cos \left( A + B \right) + \cos \left( A - B \right)} = \tan A\]
Prove that:
Prove that:
sin2 B = sin2 A + sin2 (A − B) − 2 sin A cos B sin (A − B)
Prove that:
\[\tan\frac{\pi}{12} + \tan\frac{\pi}{6} + \tan\frac{\pi}{12}\tan\frac{\pi}{6} = 1\]
Prove that:
tan 36° + tan 9° + tan 36° tan 9° = 1
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 angle \[\theta\] is divided into two parts such that the tangents of one part is \[\lambda\] times the tangent of other, and \[\phi\] is their difference, then show that\[\sin\theta = \frac{\lambda + 1}{\lambda - 1}\sin\phi\]
If α and β are two solutions of the equation a tan x + b sec x = c, then find the values of sin (α + β) and cos (α + β).
If x cos θ = y cos \[\left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)\]then write the value of \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\]
Write the maximum and minimum values of 3 cos x + 4 sin x + 5.
If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β).
The value of \[\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}\]
If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
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 tan θ1 tan θ2 = k, then \[\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =\]
If tan (π/4 + x) + tan (π/4 − x) = a, then tan2 (π/4 + x) + tan2 (π/4 − x) =
If cos (A − B) \[= \frac{3}{5}\] and tan A tan B = 2, then
If \[\tan\alpha = \frac{x}{x + 1}\] and \[\tan\alpha = \frac{x}{x + 1}\], then \[\alpha + \beta\] is equal to
If sinθ + cosθ = 1, then find the general value of θ.
Find the most general value of θ satisfying the equation tan θ = –1 and cos θ = `1/sqrt(2)`.
Find the general solution of the equation `(sqrt(3) - 1) costheta + (sqrt(3) + 1) sin theta` = 2
[Hint: Put `sqrt(3) - 1` = r sinα, `sqrt(3) + 1` = r cosα which gives tanα = `tan(pi/4 - pi/6)` α = `pi/12`]
If f(x) = cos2x + sec2x, then ______.
[Hint: A.M ≥ G.M.]
If tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to ______.
If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.
If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.
The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is ______.
