A simple trigonometry problem

Geometry Level 2

Find the value of 12 s i n 2 6 1 0 + 8 + 12 s i n 2 2 9 0 9 c o s 2 1 3 0 + 1 + 9 c o s 2 7 7 0 \frac{12sin^{2} 61^{0} + 8 + 12sin^{2} 29^{0}}{9cos^{2} 13^{0} + 1 + 9cos^{2} 77^{0}} .

3 4 1 2

Manish Mayank by Manish Mayank , 20, India

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1 solution

Manish Mayank
Nov 29, 2014

12 s i n 2 6 1 0 + 8 + 12 s i n 2 2 9 0 9 c o s 2 1 3 0 + 1 + 9 c o s 2 7 7 0 \frac{12sin^{2} 61^{0} + 8 + 12sin^{2} 29^{0}}{9cos^{2} 13^{0} + 1 + 9cos^{2} 77^{0}} = 12 s i n 2 6 1 0 + 8 + 12 c o s 2 6 1 0 9 s i n 2 7 7 0 + 1 + 9 c o s 2 7 7 0 \frac{12sin^{2} 61^{0} + 8 + 12cos^{2} 61^{0}}{9sin^{2} 77^{0} + 1 + 9cos^{2} 77^{0}} = 12 ( s i n 2 6 1 0 + c o s 2 6 1 0 ) + 8 9 ( s i n 2 7 7 0 + c o s 2 7 7 0 ) + 1 \frac{12(sin^{2}61^{0} + cos^{2}61^{0}) + 8}{9(sin^{2}77^{0} + cos^{2}77^{0}) + 1} = 12 + 8 9 + 1 \frac{12+8}{9+1} = 20 10 \frac{20}{10} = 2 \boxed{2}

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