Question

. Prove that sin²A + cos² A= 1​

Answer 1

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Let a, b, c be lengths of right angled triangle

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By definition

$sinθ = \frac {b}{c}(\frac {hypotenuse}{opposite side})$

$cosθ = \frac {a}{c}(\frac{hypotenuse}{adjacent side})$

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$sin²θ + cos²θ = \frac {b²}{c²} + \frac {a²}{c²}$

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From Pythagoras theorem,

c² = a² + b²

$∴ \frac{a² + b²}{c²}= 1$

$sin²θ + cos²θ = 1$

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Hence, proved.