What is the general solution for 2cot^2(x)-5=sec^2(x)-tan^2(x) ?

The general solution for 2cot^2(x)-5=sec^2(x)-tan^2(x) is x= pi/6+pin,x=(5pi)/6+pin

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2cot^2(x)-5=sec^2(x)-tan^2(x)

2 cot^{2} (x) - 5 = sec^{2} (x) - tan^{2} (x)

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Solution steps

2 cot^{2} (x) - 5 = sec^{2} (x) - tan^{2} (x)

Subtract

sec^{2} (x) - tan^{2} (x)

from both sides

2 cot^{2} (x) - 5 - sec^{2} (x) + tan^{2} (x) = 0

Rewrite using trig identities

- 6 + 2 cot^{2} (x) = 0

Solve by substitution

cot (x) = 3, cot (x) = - 3

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = - 3 : x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

9 (1 - sin (θ)) = 9

sin (θ) = \frac{15.226}{10.6}

cos (4 x) - 1 = sin (4 x)

csc^{2} (x) - csc (x) - 20 = 0

(sin (x) - 1) (2 sin (x) + 1) = 0

What is the general solution for 2cot^2(x)-5=sec^2(x)-tan^2(x) ?
The general solution for 2cot^2(x)-5=sec^2(x)-tan^2(x) is x= pi/6+pin,x=(5pi)/6+pin