What is the general solution for 25cot^2(x)-16=0 ?

The general solution for 25cot^2(x)-16=0 is x=0.89605…+pin,x=2.24553…+pin

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25cot^2(x)-16=0

25 cot^{2} (x) - 16 = 0

x = 0.89605 \dots + πn, x = 2.24553 \dots + πn

Solution steps

25 cot^{2} (x) - 16 = 0

Solve by substitution

cot (x) = \frac{4}{5}, cot (x) = - \frac{4}{5}

cot (x) = \frac{4}{5} : x = arccot (\frac{4}{5}) + πn

cot (x) = - \frac{4}{5} : x = arccot (- \frac{4}{5}) + πn

Combine all the solutions

x = arccot (\frac{4}{5}) + πn, x = arccot (- \frac{4}{5}) + πn

Show solutions in decimal form

x = 0.89605 \dots + πn, x = 2.24553 \dots + πn

- 9 cos^{2} (θ) + 9 = 16 sin (θ) - 7

3 + 2 cos (x) = 0

sin (θ) = - 0.5

2 sin^{2} (3 x) + sin (3 x) - 1 = 0

2 cos (3 x) = - 2

What is the general solution for 25cot^2(x)-16=0 ?
The general solution for 25cot^2(x)-16=0 is x=0.89605…+pin,x=2.24553…+pin