Advertisements
Advertisements
प्रश्न
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
उत्तर
To Prove: `((1 + tan^2 A))/((1 + cot^2 A))` = sec2 A – 1
LHS.
We have, `(((1 + sin^2 A)/(cos^2 A)))/(((1 + cos^2 A)/(sin^2 A)))`
= `[(((cos^2 A + sin^2 A))/(cos^2 A))/(((sin^2 A + cos^2 A))/(sin^2 A))]`
= `((1/cos^2 A))/((1/sin^2 A))` ...[As sin2 A + cos2 A = 1]
= `((sin^2 A))/((cos^2 A))`
= tan2 A
= sec2 A – 1
Hence, proved.
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
Prove the following trigonometric identities.
`(1 + sin theta)/cos theta + cos theta/(1 + sin theta) = 2 sec theta`
Prove the following identities:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
If \[\cos A = \frac{7}{25}\] find the value of tan A + cot A.
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Choose the correct alternative:
1 + tan2 θ = ?
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
If x = a tan θ and y = b sec θ then
Choose the correct alternative:
cos 45° = ?
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
