What is the general solution for sec(x)cot(x)= 7/6 ?

The general solution for sec(x)cot(x)= 7/6 is x=1.02969…+2pin,x=pi-1.02969…+2pin

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sec(x)cot(x)= 7/6

sec (x) cot (x) = \frac{7}{6}

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

Solution steps

sec (x) cot (x) = \frac{7}{6}

Subtract

\frac{7}{6}

from both sides

sec (x) cot (x) - \frac{7}{6} = 0

Simplify

sec (x) cot (x) - \frac{7}{6} : \frac{6 sec ( x ) cot ( x ) - 7}{6}

\frac{6 sec ( x ) cot ( x ) - 7}{6} = 0

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

6 sec (x) cot (x) - 7 = 0

Express with sin, cos

\frac{6 - 7 sin ( x )}{sin ( x )} = 0

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

6 - 7 sin (x) = 0

Move

6

to the right side

- 7 sin (x) = - 6

Divide both sides by

- 7

sin (x) = \frac{6}{7}

Apply trig inverse properties

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

Show solutions in decimal form

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

tan (x) cos (x) = 0

sin^{2} (x) - 3 sin (x) cos (x) + 2 cos^{2} (x) = 0

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

sin (t) = - \frac{2}{2}

9 cos (2 θ) = 9 cos^{2} (θ) - 4

What is the general solution for sec(x)cot(x)= 7/6 ?
The general solution for sec(x)cot(x)= 7/6 is x=1.02969…+2pin,x=pi-1.02969…+2pin