Express the sum or difference as a product of sines andor co

Express the sum or difference as a product of sines and/or cosines.

cos(2) - cos(4)

Find the exact value of the expression.

tan 75°

Solve the equation on the interval 0 < 2.

cos - sin = 0

Express the product as a sum containing only sines or cosines.

2 cos(7) cos

Solve the equation on the interval 0 < 2.

cos = sin

Use the Half-angle Formulas to find the exact value of the trigonometric function.

cos 22.5°

questions which are visible , iam giving the solution.

1) Express the sum or difference as a product of sines and/or cosines.

cos(2) - cos(4)

use the trig, formula : cosA - cosB =2sin(A+B)/2sin(B-A)/2

So, cos(2) - cos(4) = 2sin( 2+4)/2sin(2 - 4 )/2

= 2sin3sin(-)

= -2sin3sin

Find the exact value of the expression.

tan 75° = tan( 45 +30)

use trig formula : tan(a +b) = (tana +tanb)/( 1- tana*tanb)

tan 75° = tan( 45 +30) = (tan45 +tan30)/( 1- tan45tan30)

= ( 1 + 1/sqrt3)/( 1- 1/sqrt3)

= (sqrt3 +1)/(sqrt3 -1)

3) Solve the equation on the interval 0 < 2.

cos - sin = 0

divide both sides by cos:

1- tan =0

tan = 1

= tan^-1(1) = pi/4 . pi+pi/4 ( tan is +ve in Ist and IIIrd quadrant)

= pi/4 , 5pi/4

4) Express the product as a sum containing only sines or cosines.

2 cos(7) cos

Use the trig formula : cosX cosY = (1/2) [ cos (X - Y) + cos (X + Y) ]

So, we get 2 cos(7) cos = 2{ 1/2 [ cos(7 - ) +cos(7+) ]

= cos6 +cos8