prove sin^2+cos^2=1
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Answered by
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Answer:
Let there be a ΔABC right angled at B. Then, AC is the hypotenuse.
Let AB be the base and BC be the perpendicular. Let ∠A=θ
sinθ=perpendicular/hypotenuse
=BC/AC
cosθ=base/hypotenuse
=AB/AC
sin²θ+cos²θ=(BC²+AB²)/AC²
=AC²/AC² [AB²+BC²=AC²;Pythagoras theorem]
=1
HENCE PROVED.
Answered by
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Step-by-step explanation:
sin^2 theta + cos^2 theta =1
as we know that
sin theta=opp side/hyp
cos theta=adj side / hyp
then,opp side^2/hyp^2+adj side^2/hyp^2
=opp side ^2 +adj side^2 / hyp^2
=hyp^2/hyp^2=1
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