If, in general, the value of sin A is known but the value of A is not known, then how many values of tan can be calculated?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Solution:
We know that:
tan A = sin A / cos A

Hence, if sin A is known and A is not known, the value of cos A cannot be determined. Therefore, we cannot determine the value of tan A exactly.

However, we can determine the possible values of tan A based on the quadrant in which angle A lies, as the signs of sin A and cos A depend on the quadrant.

- If sin A is positive, A lies in either the first or second quadrant.
- In the first quadrant, both sin A and cos A are positive, so tan A can be calculated as sin A / cos A.
- In the second quadrant, sin A is positive but cos A is negative, so tan A can be calculated as sin A / cos A, but its sign is negative. Therefore, we get two possible values of tan A.
- If sin A is negative, A lies in either the third or fourth quadrant.
- In the third quadrant, both sin A and cos A are negative, so tan A can be calculated as sin A / cos A, but its sign is positive. Therefore, we get two possible values of tan A.
- In the fourth quadrant, sin A is negative but cos A is positive, so tan A can be calculated as sin A / cos A, but its sign is negative. Therefore, we get two possible values of tan A.

Hence, in general, if the value of sin A is known but the value of A is not known, we can calculate two possible values of tan A. Therefore, the correct answer is option B - 2.

Answer

Let ABC be triangle. Then sinA is the ratio w.r.t A so tanA is defined so the remaining angle is B that also defined. so answer is 2

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