Advertisements
Advertisements
प्रश्न
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
उत्तर
Divide the given equation by 2 to get
`sqrt(3)/2 cos theta + 1/2 sin theta = 1/sqrt(2)`
or `cos pi/6 cos theta + sin pi/6 sin theta = cos pi/4`
or `cos(pi/6 - theta) = cos pi/4` or `cos(theta - pi/6) = cos pi/4`
Thus, the solution is given by, i.e., θ = `2 m pi +- pi/4 + pi/6`
Hence, the solution is
θ = `2 m pi + pi/4 + pi/6` and `2 m pi - pi/4 + pi/6,` i.e., `theta = 2 m pi + (5pi)/12` and `theta = 2 m pi - pi / 12`
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation `cot x = -sqrt3`
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 (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
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:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
If tan x = \[x - \frac{1}{4x}\], then sec x − tan 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
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:
\[\cot x + \tan x = 2\]
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
