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प्रश्न
If 8 tanθ = 15, find (i) sinθ, (ii) cotθ, (iii) sin2θ - cot2θ
उत्तर
8tan θ = 15
⇒ tan θ = `(15)/(8) = "Perpendicular"/"Base"`
Hypotenuse
= `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt(15^2 + 8^2)`
= `sqrt(225 + 64)`
= `sqrt(289)`
= 17
(i) sin θ = `"Perpendicular"/"Hypotenuse" = (15)/(17)`
cot θ = `(1)/"tan θ " = (8)/(15)`
(iii) sin2θ - cot2θ
= (sin θ + cot θ)(sin θ - cot θ)
= `(15/17 + 8/15)(15/17 - 8/15)`
= `((225 + 136)/225)((225 - 136)/225)`
= `(361/225)(89/255)`
= `(32129)/(65025)`.
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