What is the general solution for (cot(θ))/(sec(θ))=sin(θ) ?

The general solution for (cot(θ))/(sec(θ))=sin(θ) is θ= pi/4+pin,θ=(3pi)/4+pin

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(cot(θ))/(sec(θ))=sin(θ)

\frac{cot ( θ )}{sec ( θ )} = sin (θ)

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

Solution steps

\frac{cot ( θ )}{sec ( θ )} = sin (θ)

Subtract

sin (θ)

from both sides

\frac{cot ( θ )}{sec ( θ )} - sin (θ) = 0

Simplify

\frac{cot ( θ )}{sec ( θ )} - sin (θ) : \frac{cot ( θ ) - sin ( θ ) sec ( θ )}{sec ( θ )}

\frac{cot ( θ ) - sin ( θ ) sec ( θ )}{sec ( θ )} = 0

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

cot (θ) - sin (θ) sec (θ) = 0

Express with sin, cos

\frac{cos ^{2} ( θ ) - sin ^{2} ( θ )}{cos ( θ ) sin ( θ )} = 0

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

cos^{2} (θ) - sin^{2} (θ) = 0

Rewrite using trig identities

cos (2 θ) = 0

General solutions for

cos (2 θ) = 0

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

Solve

2 θ = \frac{π}{2} + 2 πn : θ = \frac{π}{4} + πn

Solve

2 θ = \frac{3 π}{2} + 2 πn : θ = \frac{3 π}{4} + πn

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

16 sin (2 x) = 0

cos (2 α) + sin (α) = 0

sin (9 0^{\circ} - x^{\circ}) = \frac{4}{5}

sin (x) = sin (8 0^{\circ})

tan (A) = 2.0503

What is the general solution for (cot(θ))/(sec(θ))=sin(θ) ?
The general solution for (cot(θ))/(sec(θ))=sin(θ) is θ= pi/4+pin,θ=(3pi)/4+pin