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| 1. |
If 1+sin^2A=3 sinA cosA, then prove that tanA=1or tanA=1/2 |
| Answer» 1 + sin^2 A = 3 sin A cos A. 1 - 3 sin A cos A + sin^2 A = 0. 1/cos^2 A - 3 sin A cos A /cos^2 A + sin^2 A/cos^2 A = 0. sec^2 A - 3 tan A + tan^2 A = 0. 1 + tan^2 A + tan^2 A - 3 tan A = 0. 2 tan^2 A - 3 tan A + 1 = 0. (S = -3, P = 2, No. = -2, -1.) 2 tan^2 A - 2 tan A - tan A + 1 = 0. 2 tan A (tan A - 1) - 1 (tan A - 1) = 0. (2 tan A - 1) (tan A - 1) = 0. Therefore, tan A = 1, 1/2// | |