Advertisements
Advertisements
प्रश्न
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
Advertisements
उत्तर
sin θ = `-1/sqrt(2)`
We know that principal of sin θ lies in `[ - pi/2, pi/2]`
sin θ = `- 1/sqrt(2 < 0`
∴ The principal value of sin θ lies in the IV quadrant.
sin θ = `- 1/sqrt(2)`
= `- sin(pi/4)`
sin θ = `sin (- pi/4)`
Hence θ = `- pi/4` is the principal solution.
The general solution is
θ = nπ + (– 1)n . `( pi/4)`, n ∈ Z
θ = `"n"pi + (- 1)^("n" + 1) * pi/4`, n ∈ Z
APPEARS IN
संबंधित प्रश्न
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
Prove that:
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
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
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:
Solve the following equation:
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the number of points of intersection of the curves
If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
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`
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
