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Question
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
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Solution
From diagram,
sin B = `"AC"/"BC"`, sin C = `"AB"/"BC"
L.H.S = sin2 B + sin2 C
= `"AC"^2/"BC"^2 + "AB"^2/"BC"^2`
= `("AC"^2 + "AB"^2)/"BC"^2`
= `"BC"^2/"BC"^2`
= 1
= R.H.S
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