Solution
Solution
+1
Degrees
Solution steps
Subtract from both sides
Let:
Rewrite using trig identities
Use the Double Angle identity:
Expand
Distribute parentheses
Apply minus-plus rules
Simplify
Group like terms
Add the numbers:
Factor
Rewrite as
Factor out common term
Divide the numbers:
Remove parentheses:
Solve by substitution
Let:
Remove square roots
Subtract from both sides
Simplify
Square both sides:
Expand
Apply exponent rule: if is even
Apply radical rule:
Apply exponent rule:
Multiply fractions:
Cancel the common factor:
Expand
Apply exponent rule: if is even
Solve
Move to the right side
Subtract from both sides
Simplify
Move to the left side
Subtract from both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
For the solutions are
Verify Solutions:TrueFalse
Check the solutions by plugging them into
Remove the ones that don't agree with the equation.
Plug in True
Apply radical rule:
Apply exponent rule:
Multiply fractions:
Cancel the common factor:
Join
Convert element to fraction:
Since the denominators are equal, combine the fractions:
Multiply the numbers:
Subtract the numbers:
Add similar elements:
Plug in False
Remove parentheses:
Apply exponent rule: if is even
Apply radical rule:
Apply exponent rule:
Multiply fractions:
Cancel the common factor:
Join
Convert element to fraction:
Since the denominators are equal, combine the fractions:
Multiply the numbers:
Subtract the numbers:
Add similar elements:
Apply exponent rule:
Multiply
Multiply fractions:
Multiply:
Cancel the common factor:
The solution is
Substitute back
Apply trig inverse properties
General solutions for
Combine all the solutions
Substitute back
Simplify
Use the following trivial identity:
Multiply both sides by
Multiply both sides by
Simplify
Simplify
Divide the numbers:
Simplify
Multiply fractions:
Cancel the common factor:
Multiply the numbers:
Simplify
Use the following trivial identity:
Multiply both sides by
Multiply both sides by
Simplify
Simplify
Divide the numbers:
Simplify
Multiply the numbers:
Multiply fractions:
Cancel the common factor:
Multiply the numbers:
Popular Examples
0.322=sin(3.92232*x)solvefor x,arcsin(y)=arcsin(x)solve for solvefor x,cos(2x)= 1/2solve for (10710*cos(2*a))+336.22=0tan(θ)= 2/(-2sqrt(3))
Frequently Asked Questions (FAQ)
What is the general solution for cos(x/2)=sqrt((1-cos(x))/2) ?
The general solution for cos(x/2)=sqrt((1-cos(x))/2) is x= pi/2+4pin,x=4pi-pi/2+4pin