What is the general solution for 5sin(x)=3,sec(x)-tan(x) ?

The general solution for 5sin(x)=3,sec(x)-tan(x) is No Solution for x\in\mathbb{R}

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5sin(x)=3,sec(x)-tan(x)

5 sin (x) = 3, sec (x) - tan (x)

No Solution for x \in R

Solution steps

5 sin (x) = 3, sec (x) - tan (x)

Divide both sides by

5

5 sin (x) = 3

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{3}{5}

Simplify

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

Apply trig inverse properties

sin (x) = \frac{3}{5}

General solutions for

sin (x) = \frac{3}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{3}{5}) + 2 πn, x = π - arcsin (\frac{3}{5}) + 2 πn

x = arcsin (\frac{3}{5}) + 2 πn, x = π - arcsin (\frac{3}{5}) + 2 πn

Solutions for the range

sec (x) - tan (x)

No Solution for x \in R

7 sin (x) + 2 = 0

cos (x + x) + cos (x) = 0

sin (x + 3 0^{\circ}) = cos (x + 6 0^{\circ})

cos (5 x + 4 0^{\circ}) = \frac{3}{5}

cos (4 x) + cos (2 x) + 1 = 0

What is the general solution for 5sin(x)=3,sec(x)-tan(x) ?
The general solution for 5sin(x)=3,sec(x)-tan(x) is No Solution for x\in\mathbb{R}