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Popular >

tan^2(x)+csc^2(x)-3=0

Solution

tan^{2} (x) + csc^{2} (x) - 3 = 0

Solution

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

+1

Solution steps

tan^{2} (x) + csc^{2} (x) - 3 = 0

Rewrite using trig identities

- 3 + csc^{2} (x) + \frac{1}{- 1 + csc ^{2} ( x )} = 0

Solve by substitution

csc (x) = 2, csc (x) = - 2

csc (x) = 2 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

csc (x) = - 2 : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

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