Question

Question #d49bf

Answer 1

`= (cos (a + b)(cos (a - b)`

Explanation:

Use these trig identities:
cos (a + b) = cos a.cos b - sin a.sin b
cos (a - b) = cos a.cos b + sin a.sin b)
In this case:
`(cos a.cos b)^2 - (sin a.sin b)^2 =`
`= (cos a.cos b - sin a.sin b)(cos a.cos b + sin a.sin b) =`
`= cos (a + b)(cos (a - b)`

Answer 2

`(cosacosb)^2-(sinasinb)^2`

`=cos^2acos^2b-sin^2asin^2b`

`=cos^2a(1-sin^2b)-(1-cos^2a)sin^2b`

`=cos^2a-cos^2asin^2b-sin^2b+cos^2asin^2b`

`=cos^2a-sin^2b`

`=cos^2a-(1-cos^2b)`

`=cos^2a+cos^2b-1`