Question

Cos 105-sin 15

plis bantu.

Answer 1

Cos 105 - sin 15


cos 105 = cos (60+45)
= cos 60 cos 45 + sin 60 sin 45
= 1/2 x 1/2√2 + 1/2√3 x 1/2√2
= 1/4√2 + 1/4 √6
= 1/4 (√2+√6)

sin 15
sin 15 = sin(45-30)
= sin 45 cos 30 - cos 45 sin 30
= 1/2√2 x 1/2√3 - 1/2√2 x 1/2
= 1/4√6 - 1/4√2
= 1/4(√6-√2)

cos 105 - sin 15
= 1/4 (√2+√6) - 1/4(√6-√2)
= (1/4√2 + 1/4√6) - (1/4√6 - 1/4√2)
= 1/4√2+1/4√6 - 1/4√6 + 1/4√2
= 2/4√2
= 1/2√2

jadin cos105 - sin 15 = 1/2√2