Tricky trig -
Geometry
Level
pending
Find the value of the trigonometric expression
The answer is 1.
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1 solution
sin a + cos a
= sin a + sin(90 - a)
= 2 sin(((90 - a) + a)/2) cos (((90 - a ) - a)/2) [Sum to Product formulas]
= 2 sin 45 cos(45 - a)
= 2 sin(90 - (45 - a)) = 2 sin(45 + a)
(sin a + cos a)^2 = 2 sin^2 (45+ a)
1 + sin 2*a = 2sin^2 (45 + a)
Therefore....
2sin^2 (45 + a) - sin 2* a = 1