What is the general solution for arctan(x)=(85)/((150/2-(65/4))) ?

The general solution for arctan(x)=(85)/((150/2-(65/4))) is x=tan(68/47)

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arctan(x)=(85)/((150/2-(65/4)))

arctan (x) = \frac{85}{( \frac{150}{2} - ( \frac{65}{4} ) )}

x = tan (\frac{68}{47})

Solution steps

arctan (x) = \frac{85}{( \frac{150}{2} - ( \frac{65}{4} ) )}

Simplify

\frac{85}{\frac{150}{2} - \frac{65}{4}} : \frac{68}{47}

\frac{85}{\frac{150}{2} - \frac{65}{4}}

Divide the numbers:

\frac{150}{2} = 75

= \frac{85}{75 - \frac{65}{4}}

Join

75 - \frac{65}{4} : \frac{235}{4}

75 - \frac{65}{4}

Convert element to fraction:

75 = \frac{75 \cdot 4}{4}

= \frac{75 \cdot 4}{4} - \frac{65}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{75 \cdot 4 - 65}{4}

75 \cdot 4 - 65 = 235

75 \cdot 4 - 65

Multiply the numbers:

75 \cdot 4 = 300

= 300 - 65

Subtract the numbers:

300 - 65 = 235

= 235

= \frac{235}{4}

= \frac{85}{\frac{235}{4}}

Apply the fraction rule:

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

= \frac{85 \cdot 4}{235}

Multiply the numbers:

85 \cdot 4 = 340

= \frac{340}{235}

Cancel the common factor:

5

= \frac{68}{47}

Apply trig inverse properties

arctan (x) = \frac{68}{47}

arctan (x) = a \Rightarrow x = tan (a)

x = tan (\frac{68}{47})

x = tan (\frac{68}{47})

4 cos^{2} (2 x) = 3

- 2 sin (x) = 1

sec (x) cot (x) = - 2

sin^{2} (x) = \frac{( 4 m - 9 )}{8}

- csc (x) = 1

What is the general solution for arctan(x)=(85)/((150/2-(65/4))) ?
The general solution for arctan(x)=(85)/((150/2-(65/4))) is x=tan(68/47)