Advertisements
Advertisements
Question
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
Advertisements
Solution
`4+4 tan^2 theta `
= `4(1+ tan ^2 theta)`
=`4 sec^2 theta `
=`4/ cos^2 theta`
=`4/(2/3)^2`
=`4/((4/9))`
=`(4xx9)/4`
=9
APPEARS IN
RELATED QUESTIONS
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following trigonometric identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove the following trigonometric identity.
`(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
tan θ cosec2 θ – tan θ is equal to
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
