Question

Calculati:
a) sin 5pi/24 × cos pi/8 ;
b) cos pi/8 × cos 5pi/24 ;
c) sin 3pi/8 × sin 7pi/24
VREAU REZOLVAREA COMPLETA.COROANA GARANTAT!

Answer 1

1. = [ sin (5π/24 + π/8 ) + sin ( 5π/24 - π/8) ] / 2= [ sin 8π /24 + sin2π/24 ] /2 =
=[ sinπ/3 + sin π12 ] /2 = [√3/2 +(√6-√2) /4 ] /2 =( 2√3 + √6 -√2) /8
2 .  = [ cos ( π/8 +5π/24 ) + cos ( π/8 - 5π/24 ) ] /2 =
  =[ cos π/3 + cos( -2π/24 )] /2= [ 1/2 + cos π/12  ]  /2 = [ 1/2 +√6/4+√2 /4 ] /2 =
= [ 2 + √6 +√2 ] / 8
3 . = [cos ( 3π/8 -7π/24 ) - cos ( 3π/8+7π/24 ) ]  /2 = [ cos 2π/24 - cos 16π/24]/2
  = [ cos π/12  - cos2π/3 ] /2 = [ √6/4 +√2/4 -( -1/2) ] / 2 =[√6 + √2 - 2 ] / 8