Trigonometry_0 @ 新聞雲

標題:

Trigonometry

發問:

Let m=cosA/ cos(2B+A)(a) Prove that 1+m=2cos(A+B)cosB/cos(2B+A)(b) Prove that (1+m)tanBtan(A+B)=m-1.(c) By the results of (a) and (b), find the general solution of the equation cos45°/cos(2x+45°)=5. give answer to 3 sign. fig.-----------------just (c) part ,... 顯示更多 Let m=cosA/ cos(2B+A) (a) Prove that 1+m=2cos(A+B)cosB/cos(2B+A) (b) Prove that (1+m)tanBtan(A+B)=m-1. (c) By the results of (a) and (b), find the general solution of the equation cos45°/cos(2x+45°)=5. give answer to 3 sign. fig. -----------------just (c) part , thanks---------------------------------------- --------------------------------------------------------------------------------

最佳解答:

Put m = 5, A = 45°, B = x then, by (b) (1+5)tanxtan(45°+x)=5-1 6tanx(tan45°+tanx)/(1-tan45°tanx) = 4 3tanx(1+tanx)/(1-tanx) = 2 3tanx + 3(tanx)^2 = 2 - 2tanx 3(tanx)^2 + 5tanx - 2 = 0 (3tanx -1)(tanx+ 2) = 0 tanx = 1/3 ortanx = -2 x = 180°n + 18.4°orx = 180°n - 63.4°