Advertisements
Advertisements
प्रश्न
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Advertisements
उत्तर
Taking L.H.S.
`(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A")`
`((sin^2"A")/(cos^2"A"))/((sin^2"A")/(cos^2"A")-1)+ ((1)/(sin^2"A"))/((1)/(cos^2"A")-(1)/(sin^2"A")) ...(∵ tan "A" = (sin"A")/(cos"A"))`
= `(sin^2"A")/(sin^2 "A"- cos^2"A") + (1)/(sin^2 "A"). (sin^2"A" cos^2"A")/(sin^2"A"-cos^2"A")`
= `(sin^2"A")/(sin^2 "A"- cos^2"A") + (cos^2"A")/(sin^2 "A"- cos^2"A")`
= `(sin^2 "A"+ cos^2"A")/(sin^2"A"-cos^2"A")`
= `(1)/(1-cos^2"A"-cos^2"A") ...(∵ sin^2 "A" = 1 -cos^2"A")`
= `(1)/(1-2 cos^2 "A")`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities.
`(1/(sec^2 theta - cos theta) + 1/(cosec^2 theta - sin^2 theta)) sin^2 theta cos^2 theta = (1 - sin^2 theta cos^2 theta)/(2 + sin^2 theta + cos^2 theta)`
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
Prove the following identity :
`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
Prove that `(cosθ)/(1 + sinθ) = (1 - sinθ)/(cosθ)`.
