What is the general solution for cos^2(φ)=sin^2(φ) ?

The general solution for cos^2(φ)=sin^2(φ) is φ= pi/4+pin,φ=(3pi)/4+pin

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cos^2(φ)=sin^2(φ)

cos^{2} (φ) = sin^{2} (φ)

φ = \frac{π}{4} + πn, φ = \frac{3 π}{4} + πn

Solution steps

cos^{2} (φ) = sin^{2} (φ)

Subtract

sin^{2} (φ)

from both sides

cos^{2} (φ) - sin^{2} (φ) = 0

Rewrite using trig identities

cos (2 φ) = 0

General solutions for

cos (2 φ) = 0

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

Solve

2 φ = \frac{π}{2} + 2 πn : φ = \frac{π}{4} + πn

Solve

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

φ = \frac{π}{4} + πn, φ = \frac{3 π}{4} + πn

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

sin (x) = \frac{1}{10}

(sin (θ) - 1) (sin (θ) + 1) = 0

5 sec (θ) - 6 = 0

sec (x) = - 1, - 2 π \leq x \leq 2 π

What is the general solution for cos^2(φ)=sin^2(φ) ?
The general solution for cos^2(φ)=sin^2(φ) is φ= pi/4+pin,φ=(3pi)/4+pin