Question

if tanA + sinA = M and tanA - sinA = Nthen prove that m^2 - n^2 = 4root mn

Answer 1

tanA+sinA=m

tanA-sinA=n

m^2-n^2=4rootmn

L.H.S

M^2-n^2

(tanA+sinA)^2-(tanA-sinA)^2

tanA^2+ sinA^2+2tanA sinA-(tan^2+sin^2-2tanAsin)

tan^2+sin^2+2tanA sinA-tan^2-sinA^2+2tanA sinA

4tanA sinA

RHS

4rootmn

4root (tanA+sinA)(tanA-sinA)

4root tan^2-sin^2

4root sin^2/cos^2-sin^2

4root sin^2 (1/cos^2-1

4root sin^2 (1-cos^2/cos^2)

4root sin^2 (sin^2/cos^2)

4root sin^4/cos^2

4root (sin^2/cosA)^2

4sin^2/cosA

4sinA×sinA/cosA

4sinA.tanA

Rhs

hence proof