Sines and cosines

Geometry Level 3

sin ⁡ 6 ∘ sin ⁡ 4 2 ∘ sin ⁡ 6 6 ∘ sin ⁡ 7 8 ∘ = cos ⁡ 6 ∘ cos ⁡ 4 2 ∘ cos ⁡ 6 6 ∘ cos ⁡ 7 8 ∘ = 2 m \large \sin6^\circ \sin42^\circ \sin66^\circ \sin78^\circ= \cos6^\circ \cos42^\circ \cos66^\circ \cos78^\circ =2^m

Find m m .


The answer is -4.

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Rakshit Joshi by Rakshit Joshi , 26, India

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2 solutions

Ahmad Saad
May 17, 2016

6 Helpful 0 Interesting 0 Brilliant 0 Confused

very nice solution and interpretation!!

Rakshit Joshi - 5 years ago

@Ahmad Saad Nice solution,,,

Marvin Kalngan - 1 year, 1 month ago
Aakash Khandelwal
May 17, 2016

Use s i n ( x ) . s i n ( x + 60 ) . s i n ( 60 − x ) sin(x) . sin(x+60) . sin(60-x) = 0.25 × s i n ( 3 x ) 0.25 \times sin(3x) .

Note that x is in degrees.

Owing to above identity we multiply and divide by s i n 18 sin18 and s i n ( 54 ) sin(54) .

So we have answer as 1/16.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

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