Advertisements
Advertisements
प्रश्न
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
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
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
If tan A + sin A = m and tan A - sin A = n, then show that m2 - n2 = 4 `sqrt(mn)`.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
