Advertisements
Advertisements
प्रश्न
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Advertisements
उत्तर
LHS = \[\tan225^\circ\cot405^\circ + \tan765^\circ\cot675^\circ\]
\[ = \tan \left( 90^\circ \times 2 + 45^\circ \right)\cot \left( 90^\circ \times 4 + 45^\circ \right) + \tan \left( 90^\circ \times 8 + 45^\circ \right) \cot \left( 90^\circ \times 7 + 45^\circ \right)\]
\[ = \tan \left( 45^\circ \right) \cot \left( 45^\circ \right) + \tan \left( 45^\circ \right)\left[ - \tan \left( 45^\circ \right) \right]\]
\[ = 1 \times 1 + 1 \times \left( - 1 \right)\]
\[ = 1 - 1\]
\[ = 0\]
= RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the general solution of the equation sin 2x + cos x = 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: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
Prove that
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
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
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
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:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
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
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The smallest positive angle which satisfies the equation
If \[4 \sin^2 x = 1\], then the values of x are
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
General solution of \[\tan 5 x = \cot 2 x\] is
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
