Help with solving this equation

  • Thread starter Thread starter donjt81
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on solving the equation (sec x)^2 (tan x)^2 = 2, which can be transformed using the identity (sec x)^2 = 1 + (tan x)^2. This leads to the quadratic equation (tan x)^4 + (tan x)^2 - 2 = 0. To simplify the problem, the substitution u = tan x is recommended, allowing for easier resolution of the quadratic equation.

PREREQUISITES
  • Understanding of trigonometric identities, specifically secant and tangent functions.
  • Familiarity with quadratic equations and their solutions.
  • Knowledge of substitution methods in algebra.
  • Basic skills in solving polynomial equations.
NEXT STEPS
  • Learn how to apply trigonometric identities in equation transformations.
  • Study methods for solving quadratic equations, including factoring and the quadratic formula.
  • Explore the implications of variable substitution in algebraic equations.
  • Investigate the graphical representation of trigonometric functions and their intersections.
USEFUL FOR

Students studying trigonometry, educators teaching algebraic methods, and anyone looking to enhance their problem-solving skills in mathematics.

donjt81
Messages
70
Reaction score
0
Hi guys

I was solving a problem and I am stuck at solving this equation.

(sec x)^2 (tan x)^2 = 2
since we know that (sec x)^2 = 1 + (tan x)^2

[1 + (tan x)^2][(tan x)^2] = 2
(tan x)^2 + (tan x)^4 - 2 = 0

now what do i do...

thanks in advance.
 
Physics news on Phys.org
Substitute "u = tan x" to get a quadratic.
 

Similar threads

Calculating Trajectory Equation of Motion for a Rock Touching a Wall
  • · Replies 32 ·
2
Replies
32
Views
3K
Which Regions Can This Cannon Reach with Its Projectile?
  • · Replies 4 ·
Replies
4
Views
2K
Solved problem: Projectile in slanting tunnel
  • · Replies 6 ·
Replies
6
Views
2K
Calculate the electric field due to a charged disk (how to do the integration?)
  • · Replies 7 ·
Replies
7
Views
3K
Find smallest distance x from y-axis for both constructive & destructive interference to occur
  • · Replies 5 ·
Replies
5
Views
999
Resistance of three-dimensional objects
  • · Replies 10 ·
Replies
10
Views
1K
How Does Coriolis Force Influence Particle Motion in Rotating Systems?
  • · Replies 3 ·
Replies
3
Views
1K
Equilibrium of a rigid solid on a rod
  • · Replies 9 ·
Replies
9
Views
2K
Projectile motion when kicking a ball that lands on an upward slope
  • · Replies 13 ·
Replies
13
Views
4K
Amplitude of harmonic oscillation given position and velocity
  • · Replies 4 ·
Replies
4
Views
1K