Advertisements
Advertisements
प्रश्न
If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.
Advertisements
उत्तर
Given: sinθ = `8/17`
We know that sin2θ + cos2θ = 1
∴ cos2θ = 1 - sin2θ
∴ cos θ = `sqrt(1 - sin^2θ)`
Using given
`cosθ = sqrt(1 - (8/17)^2) = sqrt(1 - 8^2/17^2)`
∴ cos θ = `sqrt((17^2 - 8^2)/17^2) = sqrt(289 - 64)/17`
∴ cos θ = `sqrt(225)/17 = 15/17`
∴ cos θ = `15/17`
APPEARS IN
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
If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ, and sinθ.
If tanθ = 1 then, find the value of
`(sinθ + cosθ)/(secθ + cosecθ)`
Prove that:
Prove that:
(secθ - cosθ)(cotθ + tanθ) = tanθ.secθ.
Prove that:
Prove that: `1/"sec θ − tan θ" = "sec θ + tan θ"`
Prove that:
Prove that:
Choose the correct alternative answer for the following question.
1 + tan2 \[\theta\] = ?
Choose the correct alternative answer for the following question.
Prove the following.
secθ (1 – sinθ) (secθ + tanθ) = 1
Prove the following.
(secθ + tanθ) (1 – sinθ) = cosθ
Prove the following.
cot2θ – tan2θ = cosec2θ – sec2θ
Prove the following.
Prove the following.
\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]
Show that:
`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`
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
