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
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
Prove that:
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
Prove that:
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
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:
Solve the following equation:
\[\sqrt{3} \cos x + \sin x = 1\]
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
Write the number of points of intersection of the curves
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 \[\sin x - \cos x = \frac{1}{4}\].
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
The smallest positive angle which satisfies the equation
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 =
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
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:
sin θ = `-1/sqrt(2)`
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
