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

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

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

sin (x - \frac{π}{2}) tan (x) = sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

sin (x - \frac{π}{2}) tan (x) = sin (x)

Rewrite using trig identities

- cos (x) tan (x) = sin (x)

Subtract

sin (x)

from both sides

- cos (x) tan (x) - sin (x) = 0

Rewrite using trig identities

- 2 sin (x) = 0

Divide both sides by

- 2

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

8 sin (x) + 12 = 16

cos (7 x) = - 1

8 sin (t) + 8 cos (t) = 8

5 sin (\frac{π}{3} x) = 2

4 cos^{2} (x) - 5 cos (x) + 1 = 0

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