Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
LHS = cos(570°) sin(510°) + sin(−330°) cos(−390°)
= cos(570°) sin(510°) + [−sin(330°)]cos(390°)
= cos(570°) sin(510°) −sin(330°)
= cos(90° × 6 + 30°) sin(90° × 5 + 60°) − sin(90° × 3 + 60°) cos(90° × 4 + 30°)
= − cos(30°) cos(60°) − [−cos(60°)] cos(30°)]
= − cos(30°) cos(60°) + cos(30°) sin(60°)
= 0
= RHS
Hence proved .
APPEARS IN
संबंधित प्रश्न
Find the general solution of cosec x = –2
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
Find the general solution of the equation sin 2x + cos x = 0
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 \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Prove that
In a ∆ABC, prove that:
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
Which of the following is correct?
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
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
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
