Question

数学题在线求解

已知4sinθ-2cosθ/3sinθ+5cosθ =6/11,求下列各式的值。(1)5cos^2θ/sin^2θ+2sinθcosθ-3cos^2θ
(2)1-4sinθcosθ+2cos^2θ

Answer 1

把a,b,c随便代几个数字，只要满足a+b+c=0且，a,b,c都不为 0就行了，比如说2,-1,-1结果是1 解：因为a+b+c=0，所以a+b=－c，a+c

Answer 2

∵(4sinθ-2cosθ)/(3sinθ+5cosθ)=6/11
11(4sinθ-2cosθ)=6(5cosθ+3sinθ)
44sinθ-22cosθ=30cosθ+18sinθ
∴sinθ=2cosθ
∵sin²θ+cos²θ=1
4cos²θ+cos²θ=1
∴cos²θ=1/5
(1)5cos²θ/sin²θ+2sinθcosθ-3cos²θ
=5/4+cos²θ
=5/4+1/5
=1
(2)1-4sinθcosθ+2cos²θ
=1-6cos²θ
=1-6×﹙1/5﹚
=﹣1/5