Advertisements
Advertisements
प्रश्न
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Advertisements
उत्तर
LHS =\[ \tan \left( - 225^\circ \right) \cot \left( - 405^\circ \right) - \tan \left( - 765^\circ \right) \cot \left( 675^\circ \right)\]
\[ = \left[ - \tan \left( 225^\circ \right) \right]\left[ - \cot \left( 405^\circ \right) \right] - \left[ - \tan \left( 765^\circ \right) \right] \cot \left( 675^\circ \right) \left[ \because \tan \left( - x \right) = \tan \left( x \right) and \cot \left( - x \right) = - \cot \left( x \right) \right]\]
\[ = \tan \left( 225^\circ \right) \cot \left( 405^\circ \right) + \tan \left( 765^\circ \right) \cot \left( 675^\circ \right)\]
\[ = \tan \left( 90^\circ \times 2 + 45^\circ \right) \cot \left( 90^\circ \times 4 + 45^\circ \right) + \tan \left( 90^\circ \times 8 + 45^\circ \right) \cot \left( 90^\circ \times 7 + 45^\circ \right)\]
\[ = \tan \left( 45^\circ \right) \cot \left( 45^\circ \right) + \tan \left( 45^\circ \right)\left[ - \tan \left( 45^\circ \right) \right]\]
\[ = 1 \times 1 + 1 \times \left( - 1 \right)\]
\[ = 1 - 1\]
\[ = 0\]
RHS
Hence, proved .
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[\tan x = \frac{a}{b},\] show that
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
Prove that:
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If tan θ + sec θ =ex, then cos θ equals
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
Which of the following is correct?
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of points of intersection of the curves
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
The smallest value of x satisfying the equation
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 \[\sin^2 x - \cos x = \frac{1}{4}\]
The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x
