Question

prove that : 2 sin70° . sin 15° = 1/4 ​

Answer 1

Step-by-step explanation:

Sin10sin50sin70

= 1/2(2sin10sin50sin70)

And 2sinAsinB = cos (A-B) - cos (A+B)

So 1/2(2sin10sin50sin70) = 1/2(sin10{cos20 - cos120})

And cos 120 = cos (90 + 30) = 1/2

So 1/2 {sin10(cos20 +1/2)}

= 1/2sin10cos20 +1/4sin10

= 1/4(2sin10cos20) + 1/4sin10

As 2sinAcosB = sin(A+B)-sin(A-B)

= 1/4 (sin 30 -sin10) +1/4sin10

= 1/4sin30

= 1/8 = RHS