Advertisements
Advertisements
प्रश्न
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
उत्तर
L.H.S. = `(cosecA - sinA)(secA - cosA)`
= `(1/sinA - sinA)(1/cosA - cosA)`
= `((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)`
= `(cos^2A/sinA)(sin^2A/cosA)`
= sin A cos A
R.H.S. = `1/(tanA + cotA)`
= `1/(sinA/cosA + cosA/sinA)`
= `1/((sin^2A + cos^2A)/(sinAcosA))`
= `(sinAcosA)/(sin^2A + cos^2A)`
= `(sinAcosA)/1`
= sin A cos A
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
`sin^2 theta + 1/((1+tan^2 theta))=1`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
If tan A + sin A = m and tan A - sin A = n, then show that m2 - n2 = 4 `sqrt(mn)`.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
