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In ∟ABC,
☛ AB = 2 units
☛ BC = 1 unit
So,
By Pythagoras Theorem,
☛ AC² = AB² + BC²
➜ AC² = 2² + 1²
➜ AC = √5
☛ sin = Perpendicular / Hypotenuse
➜ sin = AB / Ac
➜ sin = 2 / √5
➜ sin² = 4 / 5 -----(i)
☛ cos = Base / Hypotenuse
➜ cos = BC / AC
➜ cos = 1 / √5
➜ cos² = 1 / 5 -----(ii)
Adding (i) and (ii), we get
➜ sin² + cos² = 4/5 + 1/5
➜ sin² + cos² = 4+1/5
➜ sin² + cos² = 5/5
➜ sin² + cos² = 1
Hence, The answer is 1.
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