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

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

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sin(pi/2-x)=cos^2(x)

sin (\frac{π}{2} - x) = cos^{2} (x)

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

Solution steps

sin (\frac{π}{2} - x) = cos^{2} (x)

Rewrite using trig identities

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

Subtract

cos^{2} (x)

from both sides

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

Solve by substitution

cos (x) = 0, cos (x) = 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

sin (θ) = \frac{π}{3}

tan (x) sin (x) + sin (- x) = 0, 0 \leq x \leq 2 π

tan (\frac{2 x}{3}) + 3 = 0

cos (x + \frac{3 π}{4}) - cos (x - \frac{3 π}{4}) = 0

tan (x) = \frac{50}{100}

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