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प्रश्न
If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ, and sinθ.
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उत्तर
5secθ - 12cosecθ = 0
⇒ 5secθ = 12cosecθ
⇒ `5xx1/cosθ=12xx1/sinθ`
⇒ `5/cosθ = 12/sinθ`
⇒ `sinθ/cosθ = 12/5`
⇒ tanθ = `12/5 ...[tanθ=sinθ/cosθ]`
We have,
sec2θ = 1 + tan2θ
⇒ sec2θ = 1 + `(12/5)^2`
⇒ sec2θ = 1 + `144/25`
⇒ sec2θ = `169/25`
Taking square root on both sides,
`sqrt(sec^2θ)=sqrt(169/25)`
∴ secθ = `13/5`
Now,
cosθ = `1/secθ`
⇒ cosθ = `1/(13/5)`
⇒ cosθ = `5/13`
Also,
`sinθ/cosθ` = tanθ
⇒ sinθ = tanθ × cosθ
⇒ sinθ = `12/5 xx 5/13 = 12/13`
Thus, the values of secθ, cosθ and sinθ are `13/5, 5/13 and 12/13` respectively.
संबंधित प्रश्न
If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tanθ.
If \[\tan \theta = \frac{3}{4}\], find the values of secθ and cosθ
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`(sinθ + cosθ)/(secθ + cosecθ)`
Prove that:
cos2θ (1 + tan2θ)
Choose the correct alternative answer for the following question.
sin \[\theta\] cosec \[\theta\]= ?
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1 + tan2 \[\theta\] = ?
Prove the following.
secθ (1 – sinθ) (secθ + tanθ) = 1
Prove the following.
(secθ + tanθ) (1 – sinθ) = cosθ
Prove the following.
sec2θ + cosec2θ = sec2θ × cosec2θ
Prove the following.
\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]
Prove the following.
If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.
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`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`
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Prove that: (sec θ – cos θ) (cot θ + tan θ) = tan θ.sec θ
Proof: L.H.S. = (sec θ – cos θ) (cot θ + tan θ)
= `(1/square - cos θ) (square/square + square/square)` ......`[∵ sec θ = 1/square, cot θ = square/square and tan θ = square/square]`
= `((1 - square)/square) ((square + square)/(square square))`
= `square/square xx 1/(square square)` ......`[(∵ square + square = 1),(∴ square = 1 - square)]`
= `square/(square square)`
= tan θ.sec θ
= R.H.S.
∴ L.H.S. = R.H.S.
∴ (sec θ – cos θ) (cot θ + tan θ) = tan θ.sec θ
