Question

Use a sim or difference identity and the given table for values of trig functions to find the exact value of cos(135+120).

Answer 1

Using Addition property:

`cos(135 + 120) = cos(135) \cdot cos(120) - sin(135) \cdot sin(120)`


`cos(135) = cos(45 + 90) = -cos(45) = -(1)/(√(2))`

`cos(120) = cos(180 - 60) = -cos(60) = -(1)/(2)`


`sin(135) = sin(45 + 90) = sin(45) = (1)/(√(2))`

`sin(120) = sin(180 - 60) = sin(60) = (√(3))/(2)`


`\therefore cos(135 + 120) = [-(1)/(√(2)) \cdot -(1)/(2)] - [(1)/(√(2)) \cdot (√(3))/(2)]`

`= (1)/(2√(2)) - (√(3))/(2√(2))`

`= (1 - √(3))/(2√(2))`