Find the exact value of cos165 degree A Squareroot 2 Square

Find the exact value of cos(165 degree). (A) Squareroot 2 + Squareroot 6/4; (B) Squareroot 2 - Squareroot 6/4; (C) Squareroot 6 - Squareroot 2/4; (D) -Squareroot 2 - Squareroot 6/4; (E) Squareroot 2 + Squareroot 6/2 Find the exact value of cos(2u) if sin(u) = 4/5 and 0

Solution

7) cos165 = cos(135 +30)

= cos135*cos30 - sin135*sin30

= cos(180-45)cos30 - sin(180 -45)sin30

= (-1/sqrt2)(sqrt3/2) - (1/sqrt2)(1/2)

= ( -sqrt3 -1)/2sqrt2)

rationalise denominator : ( -sqrt3 -1)sqrt2/2sqrt2*sqrt2

= -( sqrt6 +sqrt2)/4

Option D

8) cos2u ; sinu = 4/5

cos2u = 1- 2sin^2u

= 1 - 2(4/5)^2

= (25- 32)/25

= -7/25

This is correct solution. Plz check your question