Question

How to calculate this? `sin^2(110^@)+sin^2(200^@)`.

Answer 1

1

Explanation:

Use trig identity and properties of complementary and supplementary arcs:
`cos^2 a + sin^2 a = 1`
In this case:
`sin (110) = sin (90 + 20) = cos (20)`
`sin^2 (110) = cos^2 (20)`
`sin (200) = sin (180 + 20) = - sin (20)`
`sin^2 (200) = sin^2 (20)`
Finally:
`sin^2 (110) + sin^2 (200) = cos^2 (20) + sin^2 (20) = 1`