Advertisements
Advertisements
प्रश्न
Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
Advertisements
उत्तर
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(bb(cos^2θ) + bb(sin^2θ))/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ...............[sin2θ + cos2θ = 1]
= `1/sinθ xx 1/bbcosθ`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
If tanθ `= 3/4` then find the value of secθ.
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
`sin θ = 1/2`, then θ = ?
If 3 sin θ = 4 cos θ, then sec θ = ?
Prove that `(cot A)/(1 - tan A) + (tan A)/(1 - cot A) = 1 + tan A + cot A = sec A . "cosec" A + 1`.
If 2sin2θ – cos2θ = 2, then find the value of θ.
Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos (α - β)/2` is ______.
