Question

Prove that:
sin80 -COS110=√3sin50​

Answer 1

Hence Proved

Explanation:

• To Prove that
• Sin 80 - Cos 110 =
  `√(3)`× Sin 50
• Cos 90+∅ = -Sin ∅
• Sin 80 - Cos 90+20 =
  `√(3)`× Sin 50

• Sin 80 -(-Sin 20) =
  `√(3)`×Sin 50
• Sin 80 + Sin 20 =
  `√(3)`×Sin50
• Sin A +Sin B = 2Sin (A+B)/2Cos(A-B)/2
• 2Sin (80+20)/2Cos (80-20)/2 =
  `√(3)`×Sin50
• 2Sin 50Cos 30 =
  `√(3)`×Sin50
• Cos 30 =
  `√(3)`/2
• 2×
  `√(3)`/2×Sin50 =
  `√(3)`×Sin50
• 
  `√(3)`×Sin50 =
  `√(3)`×Sin50
• Hence proved