Prove sin²a+cos²a=1 on the chapter of trigonometry
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Sina= opposite/hypotenuse, cosa=adjacent/hypotenuse. According to Pythagoras theorem,
(Hypotenuse)^2= sum of square of its two sides.(opposite)^2+ (adjacent)^2=(hypotenuse)^2.
Therefore, sin^2a+cos^2a=1
(Hypotenuse)^2= sum of square of its two sides.(opposite)^2+ (adjacent)^2=(hypotenuse)^2.
Therefore, sin^2a+cos^2a=1
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Answer:
Step-by-step explanation:
In a triangle ABC , right angled at B
=AB square+BC square= AC square(1)
= Divide each term of eqn(1) by AC square
= AB square/AC sqaure+BC square/AC square = AC square/ AC square
= (Cos A) sqaure + (SinA) square=AC sqaure/AC square(Using applications of trignometry)
Cos square A + Sin square A = 1
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