Prove

sinA.sin(60-A).sin(60+A)=sin3A/4

Open in App

Solution

sinA . sin(60 – A) . sin(60 + A)

= sinA . (sin60 cos A – cos60 sin A) . (sin60 cos A + cos60 sin A)

= sinA . (sin²60 cos²A – cos²60 sin²A)

= sinA . {(3/4) cos²A – (1/4) sin²A)

= sinA . {(3/4) – (3/4) sin²A – (1/4) sin²A)

= sinA .{(3/4) – sin²A)

= (3/4) sinA – sin³A

= 1/4 (3 sinA – 4sin³A)

=1/4 sin3A

Suggest Corrections

Similar questions

Prove that sin A - sin 3A + sin 5A - sin 7A/ sin A - sin 3A - sin 5A +sin 7A = cot 2A.

\frac{S i n^{3} A + c o s^{3} A}{s i n A + c o s A} + \frac{S i n^{3} A - c o s^{3} A}{s i n A - c o s A} = 2

\frac{sin 3 A}{cos A} + \frac{cos 3 A}{sin A} = 2 cot 2 A

(sin 3 A + sin A) sin A + (cos 3 A - cos A) cos A = 0

$\frac{{cos}^{3} A - cos 3 A}{cos A}$ + $\frac{{sin}^{3} A - sin 3 A}{sin A} =$

Join BYJU'S Learning Program