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

The general solution for sin(θ)cos(θ)=csc(θ)sec(θ) is No Solution for θ\in\mathbb{R}

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sin(θ)cos(θ)=csc(θ)sec(θ)

sin (θ) cos (θ) = csc (θ) sec (θ)

No Solution for θ \in R

Solution steps

sin (θ) cos (θ) = csc (θ) sec (θ)

Subtract

csc (θ) sec (θ)

from both sides

sin (θ) cos (θ) - csc (θ) sec (θ) = 0

Express with sin, cos

\frac{- 1 + cos ^{2} ( θ ) sin ^{2} ( θ )}{cos ( θ ) sin ( θ )} = 0

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

- 1 + cos^{2} (θ) sin^{2} (θ) = 0

Factor

- 1 + cos^{2} (θ) sin^{2} (θ) : (sin (θ) cos (θ) + 1) (sin (θ) cos (θ) - 1)

(sin (θ) cos (θ) + 1) (sin (θ) cos (θ) - 1) = 0

Solving each part separately

sin (θ) cos (θ) + 1 = 0 or sin (θ) cos (θ) - 1 = 0

sin (θ) cos (θ) + 1 = 0 :

No Solution

sin (θ) cos (θ) - 1 = 0 :

No Solution

Combine all the solutions

No Solution for θ \in R

a, x = cos (a)

sin (\frac{1}{2} \cdot k \cdot r (1 + \frac{a ^{2}}{r ^{2}}) - 1) = π

3 sin (x) = 2 sec (x) tan (x)

12 sin (x) + 5 cos (x) = 0

sin (x) = 2 sin (2 x)

What is the general solution for sin(θ)cos(θ)=csc(θ)sec(θ) ?
The general solution for sin(θ)cos(θ)=csc(θ)sec(θ) is No Solution for θ\in\mathbb{R}