Advertisements
Advertisements
प्रश्न
Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`
Advertisements
उत्तर
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
संबंधित प्रश्न
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
Prove that:
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]
Solve the following equation:
sin x tan x – 1 = tan x – sin x
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
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.
