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prove that sin^2 a + cos^2 a=1


Since the triangle is right-angled, cos? = b/c and sin? = a/c
On squaring both we get cos2? = b2/c2 and sin2? = a2/c2
Adding together , cos2? + sin2? = (a2 + b2)/c2
Accodring to Pythagorus theorem a2 + b2 = c2 so (a2 + b2)/c2 = 1
Therefore cos2? + sin2? = 1