Solve cos^2x cos^2y-2cosx cosy cos(x y)

Question

Simplify the expression

c^{2} o^{2} s^{4} x y - 2 c^{3} o^{3} s^{3} x^{2} y^{2}

Evaluate

co s^{2} x co s^{2} y - 2 cos x cosycos x y

Rewrite the expression in exponential form

co s^{2} x co s^{2} y - 2 c^{3} o^{3} s^{3} x y x y

Multiply

More Steps

Multiply the terms

co s^{2} x co s^{2} y

Multiply the terms

c^{2} o s^{2} x o s^{2} y

Multiply the terms

c^{2} o^{2} s^{2} x s^{2} y

Multiply the terms with the same base by adding their exponents

c^{2} o^{2} s^{2 + 2} x y

Add the numbers

c^{2} o^{2} s^{4} x y

c^{2} o^{2} s^{4} x y - 2 c^{3} o^{3} s^{3} x y x y

Solution

More Steps

Multiply the terms

2 c^{3} o^{3} s^{3} x y x y

Multiply the terms

2 c^{3} o^{3} s^{3} x^{2} y \times y

Multiply the terms

2 c^{3} o^{3} s^{3} x^{2} y^{2}

c^{2} o^{2} s^{4} x y - 2 c^{3} o^{3} s^{3} x^{2} y^{2}

Show Solution

c^{2} o^{2} s^{3} x y (s - 2 co x y)

Evaluate

co s^{2} x co s^{2} y - 2 cos x cosycos x y

Multiply

More Steps

Multiply the terms

co s^{2} x co s^{2} y

Multiply the terms

c^{2} o s^{2} x o s^{2} y

Multiply the terms

c^{2} o^{2} s^{2} x s^{2} y

Multiply the terms with the same base by adding their exponents

c^{2} o^{2} s^{2 + 2} x y

Add the numbers

c^{2} o^{2} s^{4} x y

c^{2} o^{2} s^{4} x y - 2 cos x cosycos x y

Multiply

More Steps

Multiply the terms

2 cos x cosycos x y

Multiply the terms with the same base by adding their exponents

2 c^{1 + 1 + 1} os x osyos x y

Add the numbers

2 c^{3} os x osyos x y

Multiply the terms with the same base by adding their exponents

2 c^{3} o^{1 + 1 + 1} s x sys x y

Add the numbers

2 c^{3} o^{3} s x sys x y

Multiply the terms with the same base by adding their exponents

2 c^{3} o^{3} s^{1 + 1 + 1} x y x y

Add the numbers

2 c^{3} o^{3} s^{3} x y x y

Multiply the terms

2 c^{3} o^{3} s^{3} x^{2} y \times y

Multiply the terms

2 c^{3} o^{3} s^{3} x^{2} y^{2}

c^{2} o^{2} s^{4} x y - 2 c^{3} o^{3} s^{3} x^{2} y^{2}

Rewrite the expression

c^{2} o^{2} s^{3} x ys - c^{2} o^{2} s^{3} x y \times 2 co x y

Solution

c^{2} o^{2} s^{3} x y (s - 2 co x y)

Show Solution