Advertisements
Advertisements
Question
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Advertisements
Solution
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
RELATED QUESTIONS
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the principal and general solutions of the equation sec x = 2
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
Prove that
Which of the following is incorrect?
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Write the number of points of intersection of the curves
The smallest value of x satisfying the equation
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
