Saved Bookmarks
| 1. |
p isht triangle, the square of the hotethe sum of the squares of the other two sidesす721+sin2 θ = 3 sin θ cos θORtan θ =-,28,atfe る秫玑倆tan θ e: 13If 1+sin2 θ = 3 sin θ cos θ, then prove that tan θ = 1 or tan θ =-.2 |
|
Answer» 1+ + sin²x = 3 sinx cosx(1 + sin²x)² = 9 sin²x cos²x1 + sin⁴x + 2 sin²x = 9 sin²x (1 - sin²x)1 + sin⁴x + 2 sin²x = 9sin²x - 9sin⁴x10sin⁴x - 7sin²x + 1 = 0 sin²x = [ -(-7) ± √((-7)² - 4(10)(1))] / 2(10)sin²x = [ 7 ± √(49 - 40)] / 20sin²x = [ 7 ± 3] / 20sin²x = 1/2 or 1/5 sinx = ±1/√2 or ±1/√5 tanx= sinx/cosx= sinx/√(1 - sin²x) = (±1/√2)/√(1 - 1/2) OR (±1/√5)/√(1 - 1/5)= ±1 OR (±1/√5)/√(4/5)= ±1 OR ±1/2 |
|