What is the general solution for 1-1/2 cos(2x-pi/2)=0 ?

The general solution for 1-1/2 cos(2x-pi/2)=0 is No Solution for x\in\mathbb{R}

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1-1/2 cos(2x-pi/2)=0

1 - \frac{1}{2} cos (2 x - \frac{π}{2}) = 0

No Solution for x \in R

Solution steps

1 - \frac{1}{2} cos (2 x - \frac{π}{2}) = 0

Move

1

to the right side

1 - \frac{1}{2} cos (2 x - \frac{π}{2}) = 0

Subtract

1

from both sides

1 - \frac{1}{2} cos (2 x - \frac{π}{2}) - 1 = 0 - 1

Simplify

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

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

Multiply both sides by

- 2

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

Multiply both sides by

- 2

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

Simplify

cos (2 x - \frac{π}{2}) = 2

cos (2 x - \frac{π}{2}) = 2

- 1 \leq cos (x) \leq 1

No Solution for x \in R

sin (π x) = - sin (π - π x)

sin (x) cos (x) = 2 sin (x)

2 + 2 cos (θ) = 2 - 2 sin (θ)

sin (b) = 0.7245

cos (x) = \frac{6}{61}

What is the general solution for 1-1/2 cos(2x-pi/2)=0 ?
The general solution for 1-1/2 cos(2x-pi/2)=0 is No Solution for x\in\mathbb{R}