Advertisements
Advertisements
Question
Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`
Advertisements
Solution
We know cos 36° = `(sqrt(5) + 1)/4`, 36° = `pi/5`
cos 2θ = cos 36° = `cos (pi/5)`
The general solution is
2θ = `2"n"pi +- pi/5`, n ∈ Z
θ = `"n"pi +- pi/10`, n ∈ Z
APPEARS IN
RELATED QUESTIONS
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of the equation sin 2x + cos x = 0
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
Prove that
Prove that:
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 \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
If tan θ + sec θ =ex, then cos θ equals
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
If \[4 \sin^2 x = 1\], then the values of x are
The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
