Advertisements
Advertisements
Question
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
Options
0
1
2
3
Advertisements
Solution
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is 3.
Explanation:
tanx + sec = 2cosx
sin + 1 = cos2x = sinx + 1= 2 - sin2x
2sin2x + sinx -1 = 0
(2sinx - 1) (sin + 1) = 0
but sinx = -1
`x= (3pi)/2`
`sinx = 1/2 = sin(pi/6)`
therefore the general solution is,
`x = npi + (-1)^n.pi/6`
`x = ...pi/6, (5pi)/6`
therefore, the number of solutions in the given interval is 3.
APPEARS IN
RELATED QUESTIONS
Find the general solution of cosec x = –2
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
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:
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:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
Prove that:
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
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:
\[\cot x + \tan x = 2\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
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 sin α + cos α = b, then sin 2α is equal to
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
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 ______.
