What-the-exact-value-of-sin-10-2cos-10-1-2cos-10-1-

Question Number 4418 by Syaka last updated on 23/Jan/16

W h a t t h e e x a c t v a l u e o f :

s i n 10 ° (2 c o s 10 ° + 1) (2 c o s 10 ° - 1) = \dots . ?

Answered by Yozzii last updated on 24/Jan/16

s i n 10 ° (2 c o s 10 ° + 1) (2 c o s 10 ° - 1)

= s i n 10 ° (4 {c o s}^{2} 10 ° - 1)

= 2 (2 s i n 10 ° c o s 10 °) c o s 10 ° - s i n 10 °

= 2 s i n 20 ° c o s 10 ° - s i n 10 °

= {s i n (20 ° + 10 °) + s i n (20 ° - 10 °)} - s i n 10 °

= s i n 30 ° + s i n 10 ° - s i n 10 °

= 0.5

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