What is the general solution for 1-csc^2(x)=cot^2(x) ?

The general solution for 1-csc^2(x)=cot^2(x) is x= pi/2+pin

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1-csc^2(x)=cot^2(x)

1 - csc^{2} (x) = cot^{2} (x)

x = \frac{π}{2} + πn

Degrees

x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

1 - csc^{2} (x) = cot^{2} (x)

Subtract

cot^{2} (x)

from both sides

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

Rewrite using trig identities

1 - cot^{2} (x) - csc^{2} (x)

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

csc^{2} (x) - 1 = cot^{2} (x)

= - cot^{2} (x) - cot^{2} (x)

Simplify

= - 2 cot^{2} (x)

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

Divide both sides by

- 2

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

Divide both sides by

- 2

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

Divide both sides by

- 2

\frac{- 2 cot ^{2} ( x )}{- 2} = \frac{0}{- 2}

Simplify

cot^{2} (x) = 0

cot^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

cot (x) = 0

General solutions for

cot (x) = 0

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

sin (a) = 0.527

2 + 2 sin (θ) = 7 sin (θ)

sin (2 x) = 0.03

0 = - 3 + 2 sin (x)

cos (x) = \frac{( 35 )}{( 57 )}

What is the general solution for 1-csc^2(x)=cot^2(x) ?
The general solution for 1-csc^2(x)=cot^2(x) is x= pi/2+pin