Advertisements
Advertisements
प्रश्न
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Advertisements
उत्तर
L.H.S = `sqrt((1-cosA)/(1+cos A))`
`= sqrt((1-cosA)/(1+cosA) xx (1 - cos A)/(1- cos A)) = sqrt((1- cosA)^2/(1-cos^2A))`
`=sqrt((1- cosA)^2/(sin^2A)) = (1-cosA)/sin A = 1/sin A - cos A/sin A = cosec A -cot A` = R.H.S
Hence prove.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove the following identity :
`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Find the value of sin 30° + cos 60°.
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S = `square`
= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
= R.H.S
Prove that `1/("cosec" theta - cot theta)` = cosec θ + cot θ
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
If cos A + cos2A = 1, then sin2A + sin4 A = ?
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
