Advertisements
Advertisements
प्रश्न
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
In a ∆ABC, 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
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 A + cot A = 4, then tan4 A + cot4 A is equal to
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
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:
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:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
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 \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
If \[\cot x - \tan x = \sec x\], then, x is equal to
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
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:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
