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प्रश्न
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
उत्तर
`cos theta = 5/13`
`sin^2 theta = 1 - cos^2 theta = 1 - 25/169 = 144/169`
`sin theta = +- 12/13` as `theta` is acute, therefore `sintheta` must be positive
`:. sin theta = 12/13`
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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`
