Prove that sin 50 - sin 70+ sin 10 = 0
Answers
Answered by
34
First let's solve
Sin 50 - sin 70
(Use formula of sin A - sin B)
=2 cos ( (50+70)/2) sin ((50-70)/2)
=2 cos (120/2 ) sin(-20/2)
= 2 cos 60 sin (-10)
= 2 x 1/2 Sin (-10)
= - sin (10)
Now add remaining sin 10 which we had left earlier
= -sin 10 + sin 10
= 0
Hence proved
Hope it helps
Sin 50 - sin 70
(Use formula of sin A - sin B)
=2 cos ( (50+70)/2) sin ((50-70)/2)
=2 cos (120/2 ) sin(-20/2)
= 2 cos 60 sin (-10)
= 2 x 1/2 Sin (-10)
= - sin (10)
Now add remaining sin 10 which we had left earlier
= -sin 10 + sin 10
= 0
Hence proved
Hope it helps
zee95:
Hope it's clear now
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Answered by
33
sin 50 - sin 70+ sin 10 = 0
Step-by-step explanation:
to be proved
sin 50 - sin 70+ sin 10 = 0
LHS
= Sin50 - Sin70 + Sin10
= Sin(60 - 10) - Sin(60 + 10) + Sin10
Sin(A - B) = SinACosB - CosASinB
Sin(A+B) = SinACosB + CosASinB
= Sin60Cos10 - Cos60Sin10 - ( Sin60Cos10 + Cos60Sin10) + Sin10
= -2Cos60Sin10 + Sin10
Cos60 = 1/2
= -2(1/2)Sin10 + Sin10
= -Sin10 + Sin10
= 0
= RHS
QED
Proved
sin 50 - sin 70+ sin 10 = 0
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