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:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Prove that `cosA/(1+sinA) + tan A = secA`
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
Choose the correct alternative:
1 + tan2 θ = ?
Evaluate:
`(tan 65°)/(cot 25°)`
Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove that `(cos^2θ)/(sinθ) + sin θ = "cosec" θ`.
Prove that `(tan(90 - θ) + cot(90 - θ))/("cosec" θ) = sec θ`.
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
