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

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

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

cos (2 x) = sin (\frac{π}{2} - x)

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

Solution steps

cos (2 x) = sin (\frac{π}{2} - x)

Rewrite using trig identities

cos (2 x) = cos (x)

Subtract

cos (x)

from both sides

cos (2 x) - cos (x) = 0

Rewrite using trig identities

- 2 sin (\frac{3 x}{2}) sin (\frac{x}{2}) = 0

Solving each part separately

sin (\frac{3 x}{2}) = 0 or sin (\frac{x}{2}) = 0

sin (\frac{3 x}{2}) = 0 : x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}

sin (\frac{x}{2}) = 0 : x = 4 πn, x = 2 π + 4 πn

Combine all the solutions

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

Merge Overlapping Intervals

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

sin (x) = sin (5 0^{\circ})

n, y = - sin (2 (\frac{3 π}{4} + πn)) 2

tan (θ) = \frac{18}{7}

2 cos^{2} (θ) = 1 + sin (θ)

3 tan (x) = sin (x)

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