Advertisements
Advertisements
Question
Prove the following:
`(tan5"A" - tan3"A")/(tan5"A" + tan3"A") = (sin2"A")/(sin8"A")`
Solution
L.H.S. = `(tan5"A" - tan3"A")/(tan5"A" + tan3"A")`
= `((sin5"A")/(cos5"A") - (sin3"A")/(cos3"A"))/((sin5"A")/(cos5"A") + (sin3"A")/(cos3"A"))`
= `(((sin5"A" cos3"A" - sin3"A" cos5"A")/(cos5"A" cos3"A")))/(((sin5"A" cos3"A" + sin3"A" cos5"A")/(cos5"A" cos3"A"))`
= `(sin5"A" cos 3"A" - cos5"A" sin3"A")/(sin5"A" cos3"A" + cos5"A" sin3"A")`
= `(sin(5"A" - 3"A"))/(sin(5"A" + 3"A"))`
= `(sin2"A")/(sin8"A")`
= R.H.S.
APPEARS IN
RELATED QUESTIONS
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:
`(cosx + sinx)/(cosx - sinx) - (cosx - sinx)/(cosx + sinx)` = 2tan2x
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`
