What is the general solution for cot(-pi/5)-sec(x)=1.5 ?

The general solution for cot(-pi/5)-sec(x)=1.5 is x=1.92586…+2pin,x=-1.92586…+2pin

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cot(-pi/5)-sec(x)=1.5

cot (- \frac{π}{5}) - sec (x) = 1.5

x = 1.92586 \dots + 2 πn, x = - 1.92586 \dots + 2 πn

Solution steps

cot (- \frac{π}{5}) - sec (x) = 1.5

cot (- \frac{π}{5}) = - \frac{( 3 10 + 5 2 ) 5 - 5}{20}

- \frac{( 3 10 + 5 2 ) 5 - 5}{20} - sec (x) = 1.5

Move

\frac{( 3 10 + 5 2 ) 5 - 5}{20}

to the right side

- sec (x) = 2.87638 \dots

Divide both sides by

- 1

sec (x) = - 2.87638 \dots

Apply trig inverse properties

x = arcsec (- 2.87638 \dots) + 2 πn, x = - arcsec (- 2.87638 \dots) + 2 πn

Show solutions in decimal form

x = 1.92586 \dots + 2 πn, x = - 1.92586 \dots + 2 πn

\frac{1}{cos ^{2} ( x )} + (\frac{1}{2 cos ( x )}) = 0

3 sin (x) + cos (x) = 2

cos (α) = \frac{1 + \frac{1}{5}}{2}

(tan (x)) (sin^{2} (x) - a) (sec (x) - a) = 0, 0 < a < 1

sin (\frac{π}{2} (x + 1)) = \frac{2}{5}

What is the general solution for cot(-pi/5)-sec(x)=1.5 ?
The general solution for cot(-pi/5)-sec(x)=1.5 is x=1.92586…+2pin,x=-1.92586…+2pin