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

The general solution for 2sin(pi/2-θ)=sin(-θ) is θ=-1.10714…+pin

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2sin(pi/2-θ)=sin(-θ)

2 sin (\frac{π}{2} - θ) = sin (- θ)

θ = - 1.10714 \dots + πn

Solution steps

2 sin (\frac{π}{2} - θ) = sin (- θ)

Rewrite using trig identities

2 cos (θ) = - sin (θ)

Subtract

- sin (θ)

from both sides

2 cos (θ) + sin (θ) = 0

Rewrite using trig identities

2 + tan (θ) = 0

Move

2

to the right side

tan (θ) = - 2

Apply trig inverse properties

θ = arctan (- 2) + πn

Show solutions in decimal form

θ = - 1.10714 \dots + πn

csc (x) cot (x) + cot (x) = 0

tan (x) = \frac{50}{36}

- 2 + cot (x) = - 3

θ, ρ = sin (φ) sin (θ)

3 cos^{2} (x) - 6 cos (x) = - 3, 0 \leq x \leq 2 π

What is the general solution for 2sin(pi/2-θ)=sin(-θ) ?
The general solution for 2sin(pi/2-θ)=sin(-θ) is θ=-1.10714…+pin