Advertisements
Advertisements
प्रश्न
If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.
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 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: `1/"sec θ − tan θ" = "sec θ + tan θ"`
Choose the correct alternative answer for the following question.
sin \[\theta\] cosec \[\theta\]= ?
Choose the correct alternative answer for the following question.
cosec 45° =?
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.
sec2θ + cosec2θ = sec2θ × cosec2θ
Prove the following.
cot2θ – tan2θ = cosec2θ – sec2θ
Prove the following.
\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]
Prove the following.
Show that:
`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`
In ΔPQR, ∠P = 30°, ∠Q = 60°, ∠R = 90° and PQ = 12 cm, then find PR and QR.
ΔAMT∼ΔAHE, construct Δ AMT such that MA = 6.3 cm, ∠MAT=120°, AT = 4.9 cm and `"MA"/"HA"=7/5`, then construct ΔAHE.
