Question

1.已知cos(75度+α)等于三分之一,α是第三象限角,求sin(105度-α)+cos(α-105度)

Answer 1

1.

sin(105-a)+cos(a-105)

=sin(180-(75+a))+cos((a+75)-180)

=sin180 cos(75+a)-cos180 sin(75+a)+cos(a+75)cos180+sin(a+75)sin180

=(0)cos(75+a)-(-1)sin(75+a)+(-1)cos(a+75)+(0)sin(a+75)

=sin(75+a)-cos(a+75)

=√(1-cos^2(75+a))-cos(a+75)

=√(1-1/9)-1/3

=(√(8)-3)/9

2.

cosC

=cos(180-(A+B) )

=cos180 cos(A+B)+sin180 sin(A+B)

=-cos(A+B)

=-cosA cosB+sinA sinB

=-√(1-sin^2 A) cosB+sinA √(1-cos^2 B)

=-√(1-(3/5)^2) (5/13)+(3/5)√(1-(5/13)^2)

=-(4/5)(5/13)+(3/5)(12/13)

=-16/65