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

1 Answer
Nghi N
Apr 25, 2017

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#

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