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

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

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sec(x)cos(x)=sin(x)

sec (x) cos (x) = sin (x)

No Solution for x \in R

Solution steps

sec (x) cos (x) = sin (x)

Rewrite using trig identities

sec (x) cos (x)

sec (x) cos (x) = 1

sec (x) cos (x)

Express with sin, cos

sec (x) cos (x)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} cos (x)

\frac{1}{cos ( x )} cos (x) = 1

\frac{1}{cos ( x )} cos (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 cos ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= 1

= 1

= 1

1 = sin (x)

Switch sides

sin (x) = 1

General solutions for

sin (x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

No Solution for x \in R

tan (θ) - 1 - 2 = sec (θ)

3 cos (2 x) + 4 cos (4 x) - 5 = 0

cos (2 θ) = \frac{20}{29}

- 6 sin (3 x) = 0

sin (x) = \frac{2}{4}

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