Game of Identities!

Geometry Level pending

sin ⁡ 7 0 ∘ + sin ⁡ 1 0 ∘ \sin70^\circ+\sin10^\circ

If the above expression can be written as

x sin ⁡ 4 0 ∘ \sqrt { x } \sin40^\circ . Find the value of x 2 x^{2} .

Note - All the angles are in degrees.

1 5 9 3

Achal Jain by Achal Jain , 19, India

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1 solution

Achal Jain
Jul 2, 2016

We can use the identity :- s i n A + s i n B = 2 s i n A + B 2 . c o s A − B 2 sinA+sinB=\quad 2sin\frac { A+B }{ 2 } .cos\frac { A-B }{ 2 } .

Thus we would get

2 s i n 40 c o s 30 = 3 s i n 40 2sin40cos30=\sqrt { 3 } sin40 . Hence x=3 and 3 2 = 9 3^{2}=9 .

Hence answer = 9 9

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