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

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

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sec(x)+cos(x)=sin(x)tan(x)

sec (x) + cos (x) = sin (x) tan (x)

No Solution for x \in R

Solution steps

sec (x) + cos (x) = sin (x) tan (x)

Subtract

sin (x) tan (x)

from both sides

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

Express with sin, cos

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

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

1 + cos^{2} (x) - sin^{2} (x) = 0

Rewrite using trig identities

1 + cos (2 x) = 0

Move

1

to the right side

cos (2 x) = - 1

General solutions for

cos (2 x) = - 1

2 x = π + 2 πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

No Solution for x \in R

7 cos (θ) + 20 = 0

sec^{2} (x) = \frac{1}{2} csc^{2} (x) + tan^{2} (x)

x, sin (x + 3 0^{\circ}) = tan (1 0^{\circ})

4 cos (2 θ) - 3 cos (θ) + 4 = - cos (θ) + 3

cos (2 x) = 0.28

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