Solution
Solution
+1
Degrees
Solution steps
Subtract from both sides
Let:
Rewrite using trig identities
Use the Double Angle identity:
Simplify
Convert element to fraction:
Since the denominators are equal, combine the fractions:
Expand
Expand
Apply the distributive law:
Apply minus-plus rules
Simplify
Multiply the numbers:
Apply exponent rule:
Add the numbers:
Add similar elements:
Solve by substitution
Let:
Solve
Factor
Factor out common term
Apply exponent rule:
Factor out common term
Factor
Rewrite as
Apply radical rule:
Rewrite as
Apply exponent rule:
Apply Difference of Two Squares Formula:
Using the Zero Factor Principle: If then or
Solve
Move to the right side
Subtract from both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Simplify
Cancel the common factor:
Simplify
Apply the fraction rule:
Rationalize
Multiply by the conjugate
Apply radical rule:
Solve
Move to the right side
Add to both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Simplify
Cancel the common factor:
Simplify
Multiply by the conjugate
Apply radical rule:
The solutions 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
Divide both sides by
Divide both sides by
Simplify
For the solutions are
Apply radical rule:
Apply radical rule:
The following points are undefined
Combine undefined points with solutions:
Substitute back
General solutions for
periodicity table with cycle:
Solve
General solutions for
periodicity table with cycle:
General solutions for
periodicity table with cycle:
Combine all the solutions
Substitute back
Multiply both sides by
Multiply both sides by
Simplify
Multiply both sides by
Multiply both sides by
Simplify
Simplify
Divide the numbers:
Simplify
Multiply fractions:
Multiply the numbers:
Cancel the common factor:
Multiply both sides by
Multiply both sides by
Simplify
Simplify
Divide the numbers:
Simplify
Multiply fractions:
Cancel the common factor:
Popular Examples
cos(t)=(-5)/(13), 1/2 pi<t<pi31.91cos(x)=20.487sin(x)+7sin(x)tan(x)=00=cos(20t)-cos(20.02t)2tan(2x-10)=3.4641
Frequently Asked Questions (FAQ)
What is the general solution for tan(x)=3tan(1/2 x) ?
The general solution for tan(x)=3tan(1/2 x) is x=2pin,x=(5pi)/3+2pin,x= pi/3+2pin