Advertisements
Advertisements
प्रश्न
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
Advertisements
उत्तर
L.H.S = `costheta/(1 + sintheta)`
= `costheta/(1 + sintheta) xx (1 - sintheta)/(1 - sintheta)` ......[On rationalising the denominator]
= `(costheta(1 - sintheta))/(1 - sin^2theta)`
= `(costheta(1 - sintheta))/(cos^2theta)` ......`[(because sin^2theta +cos^2theta = 1),(therefore 1 -sin^2theta = cos^2theta)]`
= `(1 - sintheta)/costheta`
= R.H.S
∴ `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
If sin θ + cos θ = `sqrt(3)`, then show that tan θ + cot θ = 1
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
(1 + sin A)(1 – sin A) is equal to ______.
