Solve 2cotx + sec^2x = 0?
I am seeking assistance with the equation (2 \cot x + \sec^2 x = 0). So far, I have rewritten it as follows:
[ 2 \cot x + \sec^2 x = 0 ] [ 2/\tan x + \tan^2 x + 1 = 0 ]
I am unsure how to proceed from here. Could someone please help me find the solution and explain each step in detail? Thank you!
1 Answers
Jan 13, 2025
Elementary, I assure you…
2cotx + sec^2x = 0
2/tanx + tan^2x + 1 = 0
Now multiply through by tanx:
tan^3x + tanx + 2 = 0
By inspection, tanx = -1 is a root, in fact the only one, as synthetic division would confirm.
But if tanx = -1, then x = (4n+3)π/4, so for example 3π/4, 7π/4 etc.
Caio!
Related Questions
Find the circumference of a circle with a radius of 5 inches. Please express your answer in terms of pi.
I need assistance with an Algebra 2 problem. The question states that the variable ( r ) varies directly with ( s ) and...
How tall is 77 inches when converted to feet?
In circle O, ST is a diameter. What is the value of x if (2x + 8) equals one of the following options: 22.0, 25.0, 25.4,...
I have the following mathematical expression: 2 log₂(2) + 2 log₂(6) - log₂(3x) = 3. Is the base indeed 2? I would appr...
I have a question regarding torque in a magnetism context. I understand that the equation τ = IABsin(θ) will be relevant...
Could you please help me find the cube roots of the complex number represented in polar form as 8(cos 216° + i sin 216°)...
Please find below the present and future values for different interest rates. Compounding and discounting occur annually...
A radio telescope features a parabolic surface, as illustrated below. Given that the telescope is 1 meter deep and 12 me...
What is the cube root of ( b^{27} )?