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Trigonometric Equations

Problems

Solving General Equations

Inverse Trigonometric Relations

Problem : Solve the following equation: sin(x)tan(x) = 0 .

Solving sin(x) = 0 , x = 0, Π . Solving tan(x) = 0 , the same solutions are reached. x = 0, Π .

Problem : Solve the following equation: cos(x) - tan2(x) = 1 .

Using the identity 1 + tan2(x) = sec2(x) , the equation cos3(x) = 1 results. Therefore cos(x) = 1 , and x = 0 .

Problem : Solve the following equation: sin2(x) - 1 = cos2(x) + 2 .

Using the identity sin2(x) + cos2(x) = 1 , the equation sin2(x) = 2 results. This equation has no solution.

Problem : Solve the following equation: 2 sec(x)sin3(x) = cos(x)tan2(x) .

Resolving everything into sines and cosines and then cancelling, we have sin(x) = . x = , .

Problem : Solve the following equation: sin(x) + sin(x)cot2(x) = sec2(x) - tan2(x) .

Factoring on the right side and the use of identities leads to the equations sin(x) = 1 . Therefore, x = .

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