(2 + sinβ)(2 – sinβ) + (2 + cosβ)(2 – cosβ)

Question

(2 + sinβ)(2 – sinβ) + (2 + cosβ)(2 – cosβ)

Answer 1

(2 + sinβ)(2 – sinβ) + (2 + cosβ)(2 – cosβ) =

= 4 − sin²β + 4 − cos²β =

= 8 − (sin²β + cos²β) =

= 8 − 1 = 7