Advertisements
Advertisements
Question
Prove that: `1/"sec θ − tan θ" = "sec θ + tan θ"`
Advertisements
Solution
LHS = `1/"sec θ − tan θ"`
LHS = `1/"sec θ − tan θ" × "sec θ + tan θ"/"sec θ + tan θ"`
LHS = `"sec θ + tan θ"/((sec θ − tan θ)(sec θ + tan θ))`
LHS = `(sec θ + tan θ)/(sec^2θ − tan^2θ) ...[(a + b)(a - b) = a^2 - b^2]`
LHS = `(sec θ + tan θ)/1 ...{(1 + tan^2θ = sec^2θ),(∴ sec^2θ − tan^2θ = 1):}`
LHS = sec θ + tan θ
RHS = sec θ + tan θ
LHS = RHS
Hence proved.
APPEARS IN
RELATED QUESTIONS
If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ, and sinθ.
Prove that:
Prove that:
Prove that:
If \[\tan\theta + \frac{1}{\tan\theta} = 2\], then show that \[\tan^2 \theta + \frac{1}{\tan^2 \theta} = 2\]
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:
sec6x – tan6x = 1 + 3sec2x × tan2x
Prove the following.
\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]
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.
Show that:
`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`
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.
