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Can anyone please help me solve this?

Can anyone please help me solve this?-example-1
User Kennis
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Squares everything and then it all work
User Mkautzm
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A)

The Pythagorean theorem states that the sum of the squared legs is the squared hypothenuse:


a^2+b^2=c^2

If we divide the whole expression by
c^2, we have


(a^2)/(c^2) + (b^2)/(c^2) = (c^2)/(c^2)

B)

The sine of x is the ratio between the opposite leg and the hypothenuse, while the cosine of x is the ratio between the adjacent leg and the hypothenues:


\sin(x) = (a)/(c),\quad \cos(x) = (b)/(c)

This means that


\sin^2(x) = \left((a)/(c)\right)^2 = (a^2)/(c^2),\quad \cos^2(x) = \left((b)/(c)\right)^2 = (b^2)/(c^2)

C)

From part B, we know that


\sin^2(x)+\cos^2(x) = (a^2)/(c^2) + (b^2)/(c^2)

From part A, we know that this sum equals


\sin^2(x)+\cos^2(x) = (a^2)/(c^2) + (b^2)/(c^2)=(c^2)/(c^2)=1

Which terminates the proof.

User Solimar
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