Question

sin e + sin 30 + sin 50 + sin 70
Show that
cos + cos 30 + cos 50 + cos 70
=tan 40​

Answer 1

L.H.S = sin 10° sin 30° sin 50° sin 70° = 1 2 12 (sin 10° sin 50° sin 70° ) = 1 2 12 (sin 50° sin 70°) sin 10° = 1 2 12 [sin (60° − 10°) sin (60° + 10°)] sin 10° = 1 2 12 [( s i n 2 60 ° − s i n 2 10 ° sin260°−sin210°)] sin 10° = 1 2 12(( 3 2 32)2 − s i n 2 10 ° sin210°) sin 10° = 1 2 12 [ 3 4 34 − s i n 2 10 ° sin210°] sin 10° = 1 8 18 (3 − 4 s i n 2 10 ° sin210°)sin 10° = 1 8 18(3 sin 10° − 4 s i n 2 10 ° sin210°) = 1 11 111 (sin 3 × 10°) = 1 8 18 (sin 30°) = 1 16 116 = R.H.SRead more on Sarthaks.com - https://www.sarthaks.com/1038653/prove-that-sin-10-sin-30-sin-50-sin-70-1-16