Advertisements
Advertisements
Question
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Advertisements
Solution
Here, 2 tan2x + sec2x = 2
Which gives tan x = `+- 1/sqrt(3)`
If we take tan x = `1/sqrt(3)`
Then x = `pi/6` or `(7pi)/6`
Again, if we take tan x = `(-1)/sqrt(3)`
Then x = `(5pi)/6` or `(11pi)/6`
Therefore, the possible solutions to the above equations are
x = `pi/6, (5pi)/6, (7pi)/6` and `(11pi)/6` where 0 ≤ x ≤ 2π.
APPEARS IN
RELATED QUESTIONS
Find the general solution of the equation sin 2x + cos x = 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 \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that:
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
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
Prove that:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
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:
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:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
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.
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
The smallest positive angle which satisfies the equation
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
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 =
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
sin 5x − sin x = cos 3
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
The minimum value of 3cosx + 4sinx + 8 is ______.
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
