Advertisements
Advertisements
प्रश्न
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
Advertisements
उत्तर
`(sec theta -1)/( sec theta +1)`
= `((1/cos theta - 1/1))/((1/ costheta + 1/1))`
=`(((1- cos theta)/cos theta))/(((1+ cos theta)/cos theta))`
=`(1- cos theta)/(1+ cos theta)`
=`((1/1-2/3))/((1/1+2/3)`
=`((1/3))/((5/3))`
=`1/5`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
cos θ . sec θ = ?
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
