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

The general solution for cos(pi+x)+sin(x-pi/2)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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cos(pi+x)+sin(x-pi/2)=1

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

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

Solution steps

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

Rewrite using trig identities

- 2 cos (x) = 1

Subtract

1

from both sides

- 2 cos (x) - 1 = 0

Move

1

to the right side

- 2 cos (x) = 1

Divide both sides by

- 2

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

General solutions for

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

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

sin^{2} (a) + \frac{1}{sec ( a )} = \frac{5}{4}

\frac{csc ( x )}{cot ( x )} = 2

sin (4 x) + 6 cos (2 x) = 0

sec (θ) + tan (θ) = 0

sin (θ) = \frac{3.5}{5}

What is the general solution for cos(pi+x)+sin(x-pi/2)=1 ?
The general solution for cos(pi+x)+sin(x-pi/2)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin