Advertisements
Advertisements
प्रश्न
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Advertisements
उत्तर
Divide each term by `sqrt(2)`
`1/sqrt(2) sin theta + 1/sqrt(2) cos theta = sqrt(2)/sqrt(2)`
`sin pi/4 sin theta + cos pi/4 cos theta` = 1
`cos theta * cos pi/4 + sin theta * sin pi/4` = 1
`cos (theta - pi/4)` = 1
`cos (theta - pi/4)` = cos θ
The general solution is
`theta - pi/4` = 2nπ, n ∈ Z
θ = `2"n"pi + pi/4`, n ∈ Z
θ = `(8"n"pi + pi)/4`, n ∈ Z
θ = `(8"n" + 1) pi/4`, n ∈ Z
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
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 that
In a ∆ABC, prove that:
In a ∆ABC, prove that:
sin6 A + cos6 A + 3 sin2 A cos2 A =
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] 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:
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
If \[4 \sin^2 x = 1\], then the values of x are
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
