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

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

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sec(θ)+cos(θ)=sin(θ)tan(θ)

sec (θ) + cos (θ) = sin (θ) tan (θ)

No Solution for θ \in R

Solution steps

sec (θ) + cos (θ) = sin (θ) tan (θ)

Subtract

sin (θ) tan (θ)

from both sides

sec (θ) + cos (θ) - sin (θ) tan (θ) = 0

Express with sin, cos

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

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

1 + cos^{2} (θ) - sin^{2} (θ) = 0

Rewrite using trig identities

1 + cos (2 θ) = 0

Move

1

to the right side

cos (2 θ) = - 1

General solutions for

cos (2 θ) = - 1

2 θ = π + 2 πn

Solve

2 θ = π + 2 πn : θ = \frac{π}{2} + πn

θ = \frac{π}{2} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

No Solution for θ \in R

cos (x) = 0.98

tan (3 x + \frac{π}{2}) = - 1

15 = 60 sin (\frac{π}{15 [ 0 - d ]}) + 75

cos (θ) = \frac{2 5}{58}

tan (θ) = \frac{m ^{2} - m ^{1}}{1 + m ^{2} \cdot m ^{1}}, m^{2}

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