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Popular >

800cos(x)+800cos^2(x)-800sin^2(x)=0

Solution

800 cos (x) + 800 cos^{2} (x) - 800 sin^{2} (x) = 0

Solution

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

+1

Solution steps

800 cos (x) + 800 cos^{2} (x) - 800 sin^{2} (x) = 0

Rewrite using trig identities

- 800 + 1600 cos^{2} (x) + 800 cos (x) = 0

Solve by substitution

cos (x) = \frac{1}{2}, cos (x) = - 1

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

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