Advertisements
Advertisements
प्रश्न
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Advertisements
उत्तर
LHS=`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta ))`
=`sqrt(((1+cos theta)^2)/((1-cos theta)(1+ cos theta))) + sqrt (((1-cos theta)^2)/((1+ cos theta) (1- cos theta))`
=`sqrt(((1+cos theta)^2)/((1-cos^2 theta))) + sqrt(((1-cos theta )^2)/((1-cos^2 theta))`
=` sqrt(((1+ cos theta)^2)/(sin^2 theta))+sqrt(((1-cos theta
)^2)/sin^2 theta)`
=`((1+cos theta))/(sin theta) + ((1-cos theta))/(sin theta)`
=`(1+ cos theta +1-cos theta)/sin theta`
=`2/sin theta`
= 2cos ecθ
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities
cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1
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.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
If cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
tan (90 – θ) = ?
If 3 sin θ = 4 cos θ, then sec θ = ?
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ.
sec θ when expressed in term of cot θ, is equal to ______.
