Advertisements
Advertisements
प्रश्न
Prove the following:
`(cosx + sinx)/(cosx - sinx) - (cosx - sinx)/(cosx + sinx)` = 2tan2x
उत्तर
L.H.S. = `(cosx + sinx)/(cosx - sinx) - (cosx - sinx)/(cosx + sinx)`
= `((cosx + sinx)^2 - (cosx - sinx)^2)/((cosx - sinx)(cosx + sinx)`
= `((cos^2x + sin^2x + 2sinx cosx) - (cos^2x + sin^2x - 2sinx cosx))/(cos^2x - sin^2x)`
= `(1 + 2sinx cosx - 1 + 2sinx cosx)/(cos^2x - sin^2x)`
= `(2(2sinx cosx))/(cos^2x - sin^2x)`
= `(2sin2x)/(cos2x)`
= 2tan 2x
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following:
`(tan5"A" - tan3"A")/(tan5"A" + tan3"A") = (sin2"A")/(sin8"A")`
Prove the following:
`sin pi^"c"/8 = 1/2sqrt(2 - sqrt(2))`
Find the value of :
`cos pi/8`
Prove the following:
`(1 - cos2theta)/(1 + cos2theta)` = tan2θ
Prove the following:
`sqrt(2 + sqrt(2 + sqrt(2 + 2cos8x)` = 2 cos x
Prove the following:
`(sin3x)/cosx + (cos3x)/sinx` = 2 cot 2x
Find the value of :
`sin pi/8`
