Advertisements
Advertisements
Question
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
Options
`17/7`
`-17/7`
`7/17`
`-7/17`
Advertisements
Solution
`"tan"(2"tan"^-1 (1/5) - pi/4) = \underline(-7/17)`.
Explanation:
`tantheta = 1/5`
`tan(2theta) = (2tantheta)/(1-tan^2theta)`
`tan(2theta) = 2(1/5)/1-(1/5)^2 = (2/5)/(1-1/25) = (2/5)/(24/25) = 2/5 xx 25/24 = 50/120 = 5/12`
`tan(2theta) = 5/12`
`tan(2theta-pi/4) = (tan(2theta)-tan pi/4)/(1+tan(2theta)tan pi/4)`
`tan(2theta - pi/4) = (5/12 -1)/(1+5/12 xx 1) = ((5-12)/12)/(1+5/12) = (-7/12)/(17/12) = -7/17`
`=-7/17`
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation:
cot θ = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation :
cosθ = `sqrt(3)/(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:
4 cos2 θ = 3
Find the general solution of the following equation:
sin θ = tan θ
State whether the following equation have solution or not?
3 tanθ = 5
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
Find the principal solutions of the following equation:
tan 3θ = - 1
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
If | x | < 1, then prove that
`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`
If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
Find the principal solutions of sin x = `-1/2`
Find the principal solutions of tan x = `-sqrt(3)`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
`int (sin (log x))^2/x` log x dx = ?
Which of the following equations has no solution?
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
Find the principal solutions of cot θ = 0
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
The number of principal solutions of tan 2θ = 1 is ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
The general solution to cos100x – sin100x = 1 is ______.
If `2sin^-1 3/7` = cos–1β, then find the value of β.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
