What is the general solution for cos(θ)csc(θ)=sin(θ)sec(θ) ?

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

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cos(θ)csc(θ)=sin(θ)sec(θ)

cos (θ) csc (θ) = sin (θ) sec (θ)

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

Solution steps

cos (θ) csc (θ) = sin (θ) sec (θ)

Subtract

sin (θ) sec (θ)

from both sides

cos (θ) csc (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

64 cos^{2} (θ) = 49, (0^{\circ} \leq, θ \leq 36 0^{\circ})

y, x = 4 sec (y)

0 = 4 cos (3 θ)

sin (θ) = \frac{3}{5}, sin (2 θ)

x, \frac{1}{6} = cos^{2} (x)

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