✔ 最佳答案
1) sin225*cos315* - tan120*/sin(-60*)tan210*
= - sin 45* cos45* - (-tan 60*) / -sin 60* tan30*
= - sin 45* cos45* - tan 60* / sin 60* tan30*
= - (√2 /2 )( √2 /2 ) - √3 / (√3 / 2 )( 1 / √3 )
= - 1/2 - 2√3
2) 5sin217*cos233*+5sin127*cos323*
= 5 ( sin37*cos53* + sin53*cos37* )
= 5 sin ( 37* + 53*)
= 5 sin 90*
= 5
3) 5sin^2θ-2sinθcosθ-3cosθ^2=0
Dividing by cosθ^2,
5tanθ^2 - 2 tanθ - 3 = 0
( 5 tanθ + 3 )( tan θ - 1 ) = 0
tan θ = -3/5 or tan θ = 1
θ = 149* , 329* or θ = 45*, 225* ( cor. to 3 s.f.)
4) 4sinA=3tanA
4 sin A = 3 sin A / cos A
4 sin A cos A = 3 sin A
sin A ( 4 cos A -3 ) = 0
sin A = 0 or cos A = 3/4
A = 180* or A = 41.4*, 319* (cor. to 3s.f.) for 0<θ<360
(5) Slove cos(3θ-45*)=1/2
3θ-45*= 60* , 300*, 420*, 660*, 780*, 1020*
3θ = 105*, 345*, 465*, 705*, 825*,1065*
θ = 35*, 115*, 155*, 235*, 275*, 355* for 0<θ<360
Sorry that I haven't come across the term "Reduction principle" but anyway, I work out all the questions as far as I know. Hope it helps.