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Question
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
Solution
∠A = 90°, cos B = `"AB"/"BC"`, cos C = `"AC"/"BC"`
∴ L.H.S = cos2 B + cos2 C
= `"Ab"^2/"BC"^2 + "AC"^2/"BC"^2`
= `("AB"^2 + "AC"^2)/"BC"^2`
= `"BC"^2/"BC"^2`
= 1
= R.H.S
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