What is the general solution for cos(θ)+sin(θ+pi/2)=1,0<= θ<2pi ?

The general solution for cos(θ)+sin(θ+pi/2)=1,0<= θ<2pi is θ= pi/3 ,θ=(5pi)/3

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cos(θ)+sin(θ+pi/2)=1,0<= θ<2pi

cos (θ) + sin (θ + \frac{π}{2}) = 1, 0 \leq θ < 2 π

θ = \frac{π}{3}, θ = \frac{5 π}{3}

Solution steps

cos (θ) + sin (θ + \frac{π}{2}) = 1, 0 \leq θ < 2 π

Rewrite using trig identities

2 cos (θ) = 1

Subtract

1

from both sides

2 cos (θ) - 1 = 0

Move

1

to the right side

2 cos (θ) = 1

Divide both sides by

2

cos (θ) = \frac{1}{2}

General solutions for

cos (θ) = \frac{1}{2}

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solutions for the range

0 \leq θ < 2 π

θ = \frac{π}{3}, θ = \frac{5 π}{3}

sin^{2} (x) + cos (2 x) = 0

42 cos (x) - 8 sin (x) cos (x) = 0

sin (x) = cos (x + \frac{π}{2})

cos (θ) = \frac{2}{3}, - \frac{5 π}{2}, 2 π

6 cos (2 x) = 32

What is the general solution for cos(θ)+sin(θ+pi/2)=1,0<= θ<2pi ?
The general solution for cos(θ)+sin(θ+pi/2)=1,0<= θ<2pi is θ= pi/3 ,θ=(5pi)/3