Solution
Solution
Solution steps
Rewrite using trig identities
Use the Sum to Product identity:
Apply trig inverse properties
Use the following trivial identity:
periodicity table with cycle:
Solve
Simplify
Add similar elements:
Apply exponent rule:
Add the numbers:
Multiply both sides by
Multiply both sides by
Simplify
Simplify
Multiply fractions:
Cancel the common factor:
Simplify
Multiply:
Remove parentheses:
Solve
Switch sides
Move to the left side
Subtract from both sides
Simplify
Write in the standard form
Solve with the quadratic formula
Quadratic Equation Formula:
For
Apply rule
Apply exponent rule: if is even
Multiply the numbers:
Add the numbers:
Separate the solutions
Remove parentheses:
Multiply the numbers:
Apply the fraction rule:
Remove parentheses:
Multiply the numbers:
Apply the fraction rule:
The solutions to the quadratic equation are:
Verify Solutions
Find undefined (singularity) points:
Take the denominator(s) of and compare to zero
Solve
Move to the right side
Subtract from both sides
Simplify
Simplify
Divide both sides by
For the solutions are
Apply radical rule:
Apply radical rule:
Apply radical rule:
Apply radical rule:
The following points are undefined
Combine undefined points with solutions:
Verify solutions by plugging them into the original equation
Check the solutions by plugging them into
Remove the ones that don't agree with the equation.
Check the solution False
Plug in
For plug in
Refine
Check the solution True
Plug in
For plug in
Refine
Popular Examples
tan(a)=1cos(2θ)=2,cos^2(θ)-1=2,(-3/5)^2-1=-7/252sin(2θ)=1,0<= θ<= 2pi2cos^2(x)-3sin(x)=314cos(θ)-5=5cos(θ)-5
Frequently Asked Questions (FAQ)
What is the general solution for arctan(2x)+arctan(x)= pi/4 ?
The general solution for arctan(2x)+arctan(x)= pi/4 is x=(sqrt(17)-3)/4