Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Advertisements
उत्तर
We need to prove `(1 + cos A)/sin A = sin A/(1 - cos A)`
Now, multiplying the numerator and denominator of LHS by `1 - cos A` we get
`(1 + cos A)/sin A = (1 + cos A)/sin A xx (1 - cos A)/(1 - cos A)`
Further using the identity, `a^2 - b^2 = (a + b)(a - b)` we get
`(1 + cos A)/sin A xx (1 - cos A)/(1 - cos A) = (1 - cos^2 A)/(sin A (1- cos A))`
`= sin^2 A/(sin A(1 - cos A))` (Using `sin^2 theta + cos^2 theta = 1`)
`= sin A/(1 - cos A)`
Hence proved
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`
Prove that `cosA/(1+sinA) + tan A = secA`
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Simplify : 2 sin30 + 3 tan45.
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
Prove that sin4A – cos4A = 1 – 2cos2A
If tan θ – sin2θ = cos2θ, then show that sin2 θ = `1/2`.
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
