Evaluate

Geometry Level 2

sin ⁡ 3 8 ∘ sin ⁡ 5 2 ∘ − cos ⁡ 3 8 ∘ cos ⁡ 5 2 ∘ = ? \sin 38^\circ \sin 52^\circ - \cos 38^\circ \cos 52^\circ = \, ?


The answer is 0.

Ojasee Duble by Ojasee Duble , 19, India

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3 solutions

Ojasee Duble
Dec 21, 2016

Since, sin 38º = sin(90º - 52º) = cos 52º

And, cos38º = cos(90º - 52º) = sin 52º

Therefore,

sin 38º sin 52º - cos 38º cos 52º = cos 52º sin 52º - sin 52º cos 52º = 0

Ans. 0

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Liam Lutton
Mar 10, 2018

cos(A + B) = cos(A)cos(B) - sin(A)sin(B), since this equation is the opposite of that, we get -cos(A + B) = sin(A)sin(B) - cos(A)cos(B) inserting our values: -cos(38 + 52) = sin(38)sin(52) - cos(38)cos(52) = -cos(90) = -0 = 0

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Marta Reece
Apr 16, 2017

sin ⁡ 3 8 ∘ sin ⁡ 5 2 ∘ − cos ⁡ 3 8 ∘ cos ⁡ 5 2 ∘ = − cos ⁡ ( 3 8 ∘ + 5 2 ∘ ) = − cos ⁡ 9 0 ∘ = 0 \sin 38^\circ \sin 52^\circ - \cos 38^\circ \cos 52^\circ =-\cos(38^\circ+52^\circ)=-\cos90^\circ=0

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