The product of sin 30 and sin 60 is same as the product of cos 60 degrees tan 30 degrees and cos 30 degrees tan 60 degrees .
The product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.
From the complementary angle theorem, we have that
sinθ = cos (90° - θ)
and
cosθ = sin (90° - θ)
By applying the theorem,
sin 30° = cos (90° - 30°)
∴ sin 30° = cos 60°
Also,
sin 60° = cos (90° - 60°)
∴ sin 60° = cos 30°
Thus, sin 30° = cos 60° and sin 60° = cos 30°
Hence, the product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.
Learn more on Sine and cosine of complementary angles here: https://brainly.com/question/16127404
