Advertisements
Advertisements
प्रश्न
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
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
If \[\tan x = \frac{a}{b},\] show that
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
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 \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
Solve the following equation:
Solve the following equation:
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 \[\cot x - \tan x = \sec x\], then, x is equal to
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
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:
If sin α + cos α = b, then sin 2α is equal to
