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प्रश्न
sin2θ + sin2(90 – θ) = ?
विकल्प
0
1
2
`sqrt(2)`
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उत्तर
1
Explanation:
(sin (90 – θ))2 = (cosθ)2
sin2 (90 – θ) = cos2θ ...(1)
sin2θ + cos2θ = 1
∴ sin2θ + sin2(90 – θ) = 1 ...From (1)
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Solution:
In Δ ABC, ∠ABC = 90°, ∠C = θ°
AB2 + BC2 = `square` .....(Pythagoras theorem)
Divide both sides by AC2
`"AB"^2/"AC"^2 + "BC"^2/"AC"^2 = "AC"^2/"AC"^2`
∴ `("AB"^2/"AC"^2) + ("BC"^2/"AC"^2) = 1`
But `"AB"/"AC" = square and "BC"/"AC" = square`
∴ `sin^2 theta + cos^2 theta = square`
