What is the general solution for sin^2(x)-cos^2(x)=0.5 ?

The general solution for sin^2(x)-cos^2(x)=0.5 is x= pi/3+pin,x=(2pi)/3+pin

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sin^2(x)-cos^2(x)=0.5

sin^{2} (x) - cos^{2} (x) = 0.5

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

Solution steps

sin^{2} (x) - cos^{2} (x) = 0.5

Rewrite using trig identities

- cos (2 x) = 0.5

Divide both sides by

- 1

cos (2 x) = - 0.5

General solutions for

cos (2 x) = - 0.5

2 x = \frac{2 π}{3} + 2 πn, 2 x = \frac{4 π}{3} + 2 πn

Solve

2 x = \frac{2 π}{3} + 2 πn : x = \frac{π}{3} + πn

Solve

2 x = \frac{4 π}{3} + 2 πn : x = \frac{2 π}{3} + πn

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

sec (x) - tan (x) = 1

7 cos^{2} (θ) + 6 cos (θ) - 12 = 7 cos (θ) - 6

sin^{2} (x) = sin (x) + 1 - sin^{2} (x)

tan^{2} (x) - 3 sec (x) + 3 = 0

cos (5 t) cos (2 t) = - sin (5 t) sin (2 t)

What is the general solution for sin^2(x)-cos^2(x)=0.5 ?
The general solution for sin^2(x)-cos^2(x)=0.5 is x= pi/3+pin,x=(2pi)/3+pin