Solve tan2A - 2tanA = -1 for 0º≤A≤360º.
Hmmm. Sensing a missing ^ character, we have
tan^2(A) - 2tanA + 1 = 0
(tanA - 1)^2 = 0
tanA = 1
So, A = 45º or 225º
or taking it at face value the way it was typed
tan 2A - 2tan A = -1
2tanA/(1-tan^2 A) - 2tanA = -1
let tanA = x for easier typing
2x/(1-x^2) - 2x = -1
times 1 - x^2
2x - 2x + 2x^3 = -1 + x^2
2x^3 - x^2 + 1 = 0
by Wolfram
http://www.wolframalpha.com/input/?i=2x%5E3+-+x%5E2%2B1%3D0
x = -.657298
tanA = -.657298
A = 146.7° or A = 326.7°
both work
a ladder leaning against a vertical wall make an angle 24 degrees with the wall.the foot of the ladder is 5 ft from the wall find the length of the ladder
You lean a ladder 6.7 m long against a wall. It makes an angle of 63 degrees with the level ground. How high up is the top of the ladder?
To solve the equation tan(2A) - 2tan(A) = -1, we will use a trigonometric identity and algebraic manipulation.
Step 1: Apply the double angle identity for tangent:
tan(2A) = (2tan(A))/(1-tan^2(A))
Step 2: Substitute tan(2A) in the equation:
(2tan(A))/(1-tan^2(A)) - 2tan(A) = -1
Step 3: Simplify the equation:
2tan(A) - 2tan^3(A) - 2tan(A) = -1
Step 4: Combine like terms:
-2tan^3(A) = -1
Step 5: Divide both sides by -2:
tan^3(A) = 1/2
Step 6: Take the cube root of both sides:
tan(A) = (1/2)^(1/3)
Step 7: Find the principal value of tan(A) using a calculator or table:
tan(A) ≈ 0.7937
Step 8: Use the inverse tangent function to find the values of A.
A ≈ arctan(0.7937)
Step 9: Check the solution for values of A between 0º and 360º using a calculator or table.
Therefore, the solutions for A that satisfy the equation are the angles approximately equal to arctan(0.7937) that lie between 0º and 360º.