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

The general solution for tan(pi/2-θ)=cos(-θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin

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tan(pi/2-θ)=cos(-θ)

tan (\frac{π}{2} - θ) = cos (- θ)

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

Solution steps

tan (\frac{π}{2} - θ) = cos (- θ)

Rewrite using trig identities

\frac{cos ( θ )}{sin ( θ )} = cos (θ)

Subtract

cos (θ)

from both sides

\frac{cos ( θ )}{sin ( θ )} - cos (θ) = 0

Simplify

\frac{cos ( θ )}{sin ( θ )} - cos (θ) : \frac{cos ( θ ) - cos ( θ ) sin ( θ )}{sin ( θ )}

\frac{cos ( θ ) - cos ( θ ) sin ( θ )}{sin ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos (θ) - cos (θ) sin (θ) = 0

Factor

cos (θ) - cos (θ) sin (θ) : - cos (θ) (sin (θ) - 1)

- cos (θ) (sin (θ) - 1) = 0

Solving each part separately

cos (θ) = 0 or sin (θ) - 1 = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

sin (θ) - 1 = 0 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

tan (x) = - \frac{24}{7}

sin^{3} (x) + sin (x) = 0

x, sin (x) = - \frac{1}{2}

81 cos^{2} (x) = 16

sec (θ) (sec (θ) - 1) = 2

What is the general solution for tan(pi/2-θ)=cos(-θ) ?
The general solution for tan(pi/2-θ)=cos(-θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin