# Solve for x sin(x)*cos(x)=( square root of 3)/4 Square both sides of the equation.
Apply the product rule to .
Simplify .
Apply the product rule to .
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Raise to the power of .
Move to the left side of the equation by subtracting it from both sides.
Replace the with based on the identity.
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Subtract from both sides of the equation.
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply .
Multiply by .
Multiply by .
Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Set up the equation to solve for .
Solve the equation for .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Evaluate .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Simplify .
Multiply by .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Set up the equation to solve for .
Solve the equation for .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Evaluate .
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify .
Multiply by .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
List all of the results found in the previous steps.
, for any integer
The complete solution is the set of all solutions.
, for any integer
Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
Exclude the solutions that do not make true.
No solution
Solve for x sin(x)*cos(x)=( square root of 3)/4

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