Trigonometry> sin10sin30sin50*sin70=...

sin10sin30sin50*sin70=

melvin , 10 Years ago

Grade 11

4 Answers

Y RAJYALAKSHMI

Last Activity: 10 Years ago

We have sinx*sin(60 – x)*sin(60 + x) = 1/4* sin3x

sin10*sin30*sin50*sin70

=1/2*sin10*sin(60 – 10)*sin(60 + 10)

=1/2*1/4*sin(3*10)

=1/2*1/4*1/2

=1/16

Sabanna

Last Activity: 7 Years ago

sin10 sin30 sin 50 sin70 = 1/16

=1/2(sin10sin50sin70)
=1/2(sin50 sin70)sin10
=1/2(sin(60-10)sin(60+10))sin 10
=1/2(sin²60-sin²10)sin10
=1/8(3/4-sin²10)sin10
=1/8(3-4sin²10)sin10
=1/8(3sin10-4sin³10)
=1/8(sin3X10)
=1/16.

jannat

Last Activity: 7 Years ago

1/2 (sin10 sin50 sin70)1/2 (sin50 sin70) sin 101/2 (sin (60-10) sin (60+10)) sin101/2 (sin^2 60 -sin^2 10) sin 101/2 (3/4-sin^2 10) sin 101/8 (3-4sin^2 10) sin101/8 (3sin10-4sin^3 10)1/8 (sin 3×10)1/16

ankit singh

Last Activity: 4 Years ago

We know that
i) sin 2A = 2sinAcosA
ii) sin(90-A)= cosA
iii) sin30=1/2
LHS = sin 10 sin30 sin50sin 70
=sin 10 × 1/2 × sin (90-40)× sin(90-20)
=1/2[sin 10 ×cos 40×cos 20]
We multiply with[2 cos 10/2cos 10]
=(1/2×1/2cos10)[2sin10cos10×cos20×cos40]

=(1/4cos10)[sin20cos20×cos40]
=(1/8cos10)[2sin20cos20×cos40]
=(1/8cos10)[sin40cos40]
=(1/16cos10)[2sin40co40]
=(1/16cos10)×sin80
=(1/16cos10)×sin(90-10)
=(1/16cos10)×cos10
=1/16