Advertisements
Advertisements
प्रश्न
If \[\tan x = \frac{a}{b},\] show that
Advertisements
उत्तर
LHS:
\[\frac{a\sin x - b\cos x}{a\sin x + b\cos x}\]
Dividing by \[b\cos x: \]
\[ = \frac{\frac{a\tan x}{b} - 1}{\frac{a\tan x}{b} + 1}\]
Substituting the value of \[\tan x\]
\[ = \frac{a^2 - b^2}{a^2 + b^2}\]
= RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation `tan x = sqrt3`
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
Which of the following is incorrect?
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the general solutions of tan2 2x = 1.
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
The minimum value of 3cosx + 4sinx + 8 is ______.
