Find the exact value of cosine equation

Question

Find the exact value of: cos(165?) − cos(75?)

Answer 1

Or

 

Starting with Chaoyou L.'s fourth line

 

-[sin (45 + 30) + cos (45 + 30]

-[sin45cos30 + sin30cos45 + cos45cos30 - sin45sin30]

-[(√2/2)(√3/2) + (1/2)(√2/2) + (√2/2)(√3/2) - (√2/2)(1/2)]

-[√6/4 + √2/4 + √6/4 - √2/4]

- 2√6/4

- √6/2

 

 

 

 

Answer 2

cos(165?) − cos(75?)

= cos (90+75)-cos75

= cos 90 cos 75 -sin90sin75 -cos75

= 0-sin75 -cos75

= - √2/2(sin75+cos 75)/(√2/2)

= - (sin45sin75+cos45cos75)/(√2/2)

=-cos( 75-45)*√2

=-cos30*√2

=-√3/2*√2

=-√6/2