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Geometry Level 1

4 sin ⁡ 2 5 ∘ sin ⁡ 3 5 ∘ sin ⁡ 8 5 ∘ sin ⁡ 7 5 ∘ = ? \large\dfrac{4\sin{25^{\circ}}\sin{35^{\circ}}\sin{85^{\circ}}}{\sin{75^{\circ}}}=\ ?


The answer is 1.

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Ikkyu San by Ikkyu San , 23, Thailand

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1 solution

Tanishq Varshney
Jun 7, 2015

its a simple identity

4 sin ⁡ ( 6 0 o − A ) sin ⁡ ( A ) sin ⁡ ( 6 0 o + A ) = sin ⁡ ( 3 A ) \large{4 \sin (60^{o}-A) \sin (A) \sin (60^{o}+A)=\sin (3A)}

here A = 2 5 0 A=25^{0} hence the numerator is sin ⁡ 7 5 o \sin 75^{o} and so is the denominator ,

the answer is 1 1

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