What is the general solution for tan(x)3cot(x)=5sec(x) ?

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

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tan(x)3cot(x)=5sec(x)

tan (x) 3 cot (x) = 5 sec (x)

No Solution for x \in R

Solution steps

tan (x) \cdot 3 cot (x) = 5 sec (x)

Subtract

5 sec (x)

from both sides

3 tan (x) cot (x) - 5 sec (x) = 0

Rewrite using trig identities

- 5 sec (x) + 3 cot (x) tan (x)

Use the basic trigonometric identity:

tan (x) = \frac{1}{cot ( x )}

= - 5 sec (x) + 3 cot (x) \frac{1}{cot ( x )}

3 cot (x) \frac{1}{cot ( x )} = 3

3 cot (x) \frac{1}{cot ( x )}

Multiply fractions:

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

= \frac{1 \cdot 3 cot ( x )}{cot ( x )}

Cancel the common factor:

cot (x)

= 1 \cdot 3

Multiply the numbers:

1 \cdot 3 = 3

= 3

= - 5 sec (x) + 3

3 - 5 sec (x) = 0

Move

3

to the right side

3 - 5 sec (x) = 0

Subtract

3

from both sides

3 - 5 sec (x) - 3 = 0 - 3

Simplify

- 5 sec (x) = - 3

- 5 sec (x) = - 3

Divide both sides by

- 5

- 5 sec (x) = - 3

Divide both sides by

- 5

\frac{- 5 sec ( x )}{- 5} = \frac{- 3}{- 5}

Simplify

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

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

sec (x) \leq - 1 or sec (x) \geq 1

No Solution for x \in R

10 cos (θ) = 5

x, cot (x) = - 1

csc^{2} (x) - 5 csc (x) = 0

sin (2 x) = 0.2

sin (2 x) = 0.9

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