Advertisements
Advertisements
प्रश्न
`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`
Advertisements
उत्तर
LHS =` 1+(cot^2 theta)/((1+ cosectheta))`
=`1+((cosec^2 theta-1))/((cosectheta++1)) (∵ cosec^2 theta - cot^2 theta =1)`
=`1+((cosectheta+1)(cosec theta-1))/((cosec theta +1))`
=`1+ (cosec theta -1)`
=` cosec theta`
=RHS
APPEARS IN
संबंधित प्रश्न
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
