Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
sin θ = tan θ
Advertisements
उत्तर
sin θ = tan θ
tan θ = `sin theta/cos theta`
sin θ = `sin theta/cos theta`
Multiply both sides by cos θ
sin θ ⋅ cos θ = sin θ
sin θ cos θ − sin θ = 0
⇒ sin θ(cos θ − 1) = 0
sin θ(cos θ − 1) = 0
Case 1: sin θ = 0
sinθ = 0 ⇒ θ = nπ, where n ∈ Z
Case 2: cosθ = 1
cos θ = 1
⇒ θ = 2nπ, where n ∈ Z
Consider excluded values (where cos θ = 0)
sin θ = `sintheta/costheta`
cos θ = 0
⇒ theta = `pi/2 + npi`, where n ∈ Z
θ = nπ, where n ∈ Z
APPEARS IN
संबंधित प्रश्न
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
tan3θ = 3 tanθ.
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation have solution or not?
3 tanθ = 5
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
Select the correct option from the given alternatives:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Find the principal solutions of sin x = `-1/2`
`int (sin (log x))^2/x` log x dx = ?
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
Which of the following equations has no solution?
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The value of sin 18° is ______.
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of 4sin2 x = 1 is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of the equation tan2 x = 1 is ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
The general solution of cot 4x = –1 is ______.
