Advertisements
Advertisements
प्रश्न
Show that:
`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`
Advertisements
उत्तर
LHS = `sqrt((1-cos"A")/(1+cos"A"))`
⇒ LHS = `sqrt((1-cos"A")/(1+cos"A")xx (1-cos"A")/(1-cos"A"))`
⇒ LHS = `sqrt(((1-cos"A")^2)/(1-cos^2"A"))`
=`sqrt(((1-cos"A")^2)/sin^2"A")` ....(sin2A =1- cos2A)
⇒ LHS = `sqrt(((1-cos"A")/sin"A")^2)`
⇒ LHS = `(1-cos"A")/sin"A" = 1/sin"A" + cos"A"/sin"A"`
⇒ LHS = `cos"ecA"-cot"A"` = RHS
Hence Proved
APPEARS IN
संबंधित प्रश्न
If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tanθ.
If \[\cot\theta = \frac{40}{9}\], find the values of cosecθ and sinθ.
If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ, and sinθ.
Prove that: `1/"sec θ − tan θ" = "sec θ + tan θ"`
Prove that:
Prove that:
Choose the correct alternative answer for the following question.
sin \[\theta\] cosec \[\theta\]= ?
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 + tanθ) (1 – sinθ) = cosθ
Prove the following.
sec2θ + cosec2θ = sec2θ × cosec2θ
Prove the following.
cot2θ – tan2θ = cosec2θ – sec2θ
Prove the following:
sec6x – tan6x = 1 + 3sec2x × tan2x
Prove the following.
\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]
Prove the following.
Choose the correct alternative:
sinθ × cosecθ =?
If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.
In ΔPQR, ∠P = 30°, ∠Q = 60°, ∠R = 90° and PQ = 12 cm, then find PR and QR.
