The domain of the trigonometry function of lies between . Tangent has period , we findd solution in any interval of length .
The domain of the trigonometric function lies between . No solution exists beyond this domain. Sine has period , we find solution in any interval of length . Sine function is positive in first and second quadrant.
The trigonometric equation is given by,
The factors of above equation are,
Consider the factors.
Add 2 both sides in equation (1).
Here the angles are in radian.
The tangent has period, , so we get all solutions of the equation by adding integer multiples of to these solutions:
The solution obtained for the factor in which sine function involved so we will get the solution in the interval of .
Add 1 to both sides in equation (2).
Taking positive sign,
Taking negative sign,
The sine has period, , but it is a square function so repeating is done every length of . So we get all solutions of the equation by adding integer multiples of to these solutions:
Therefore, the solutions of the trigonometric equation are and .
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