Solve 8 sin^2 (x) =8 cos^2 (x)

Evaluate

8 sin^{2} (x) = 8 cos^{2} (x)

Use sin^{2} (x) = 1 - cos^{2} (x) to rewrite the expression

8 - 8 cos^{2} (x) = 8 cos^{2} (x)

Move the expression to the left side

8 - 8 cos^{2} (x) - 8 cos^{2} (x) = 0

Calculate

More Steps

8 - 16 cos^{2} (x) = 0

Add or subtract both sides

- 16 cos^{2} (x) = - 8

Divide both sides

\frac{- 16 cos ^{2} ( x )}{- 16} = \frac{- 8}{- 16}

Divide the numbers

cos^{2} (x) = \frac{1}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

cos (x) = \pm \frac{1}{2}

Simplify the expression

cos (x) = \pm \frac{2}{2}

Separate the equation into 2 possible cases

cos (x) = \frac{2}{2} cos (x) = - \frac{2}{2}

Calculate

More Steps

x = {\frac{π}{4} + 2 kπ \frac{7 π}{4} + 2 kπ, k \in Z cos (x) = - \frac{2}{2}

Calculate

More Steps

x = {\frac{π}{4} + 2 kπ \frac{7 π}{4} + 2 kπ, k \in Z x = {\frac{3 π}{4} + 2 kπ \frac{5 π}{4} + 2 kπ, k \in Z

Solution

x = \frac{π}{4} + \frac{kπ}{2}, k \in Z

Alternative Form

x = 4 5^{\circ} + 9 0^{\circ} k, k \in Z

Alternative Form

x \approx 0.785398 + \frac{kπ}{2}, k \in Z

Solve the equation