Question #206419

By drawing a relevant triangle,prove that

 

tan θ = sin θ / cos θ

and

cos^2 θ + sin^2 θ = 1


1
Expert's answer
2021-06-24T11:43:39-0400

Consider the right-angled triangle ABC, with AB=1, C = 90° and A= θ°.

sinθ=BCAB=BC1=BC\sin \theta =\frac{BC}{AB}=\frac{BC}{1}=BC


cosθ=ACAB=AC1=AC\cos \theta =\frac{AC}{AB}=\frac{AC}{1}=AC


tanθ=BCAC=sinθcosθ\tan \theta =\frac{BC}{AC}=\frac{\sin \theta}{\cos \theta}


Pythagorean theorem: 1=AC2+BC2=cos2θ+sin2θ1=AC^2+BC^2=\cos ^2\theta +\sin^2\theta


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