✔ 最佳答案
1)tan(45°+x) = 2tan(45°-x)(tan45° + tanx) / (1 - tan45° tanx) = 2(tan45° - tanx) / (1 + tan45° tanx)(1 + tanx) / (1 - tanx) = 2(1 - tanx) / (1 + tanx)(1 + tanx)² = 2(1 - tanx)²tan²x + 2tanx + 1 = 2tan²x - 4tanx + 2tan²x - 6tanx + 1 = 0
2)cos4x + 4cos2x= 2cos²2x - 1 + 4cos2x= 2(2cos²x - 1)² - 1 + 4(2cos²x - 1)= 2(4cos⁴x - 4cos²x + 1) - 1 + 8cos²x - 4= 8cos⁴x - 3
3a)(tanx - sin²x) / (tanx + sin²x)= (sinx - cosx sin²x) / (sinx + cosx sin²x)= (1 - cosx sinx) / (1 + cosx sinx)= (2 - 2cosx sinx) / (2 + 2cosx sinx)= (2 - sin2x) / (2 + sin2x) + 1 - 1= 4 / (2 + sin2x) - 13b)(tanx - sin²x) / (tanx + sin²x)= 4 / (2 + sin2x) - 1When sin2x = 1 , the least value of it = 4 / (2 + 1) - 1 = 1/3
4)(sina + sinb) / (cosa + cosb)= ( 2 sin (a+b)/2 cos (a-b)/2 ) / ( 2 cos (a+b)/2 cos (a-b)/2 )= sin (a+b)/2 / cos (a+b)/2 = tan (a+b)/2 ....... (a+b)/2 ≠ π/2 since a and b are acute angle.
5)3sina - 4cosa = 4cosb - 3sinb3(sina + sinb) = 4(cosa + cosb)(sina + sinb) / (cosa + cosb) = 4/3By the result of 4) ,tan (a+b)/2 = 4/3 Sotan (a+b) = 2(4/3) / (1 - (4/3)²) = - 24/7
