Advertisements
Advertisements
प्रश्न
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = "cosec" θ - cot θ`.
Prove the following:
`sqrt((1 - cos θ)/(1 + cos θ)) = "cosec" θ - cot θ`
Advertisements
उत्तर
LHS = `sqrt((1 - cos θ)/(1 + cos θ) xx (1 - cos θ)/(1 - cos θ))`
= `sqrt((1 - cos θ)^2/(1 - cos^2θ))`
= `(1 - cos θ)/(sqrt(1 - cos^2θ))`
= `(1 - cos θ)/(sqrt(sin^2θ))`
= `(1 - cos θ)/(sin θ)`
= `(1)/(sin θ) - (cos θ)/(sin θ)`
= cosec θ − cot θ
= RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
(i)` (1-cos^2 theta )cosec^2theta = 1`
If (cot θ + tan θ) = m and (sec θ – cos θ) = n, prove that `(m^2 n)^(2//3) - (mn^2)^(2//3) = 1`.
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Evaluate:
`(tan 65^circ)/(cot 25^circ)`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
