Question

If tanA+ sinA= m, tanA- sinA=n
Prove that ( m^- n^)^=16 mn

Answer 1

m2 - n2



(tanA + sinA)2 - (tanA - sinA)2




wkt (a+b)2 - (a-b)2 =4ab = 4(tanA * sinA)




now RHS 4 root mn



=4√(mn) = 4√((tanA + sinA)(tanA - sinA))



=4√(tan2A - sin



=4√(sin2A/cos2A - sin2A)




=4√((sin2A-sin2A*cos2A)/cos2A)




= 4√sin2A(1-cos2A)/cos2A




=4*sin2A/cosA



=4*sinA*sinA/cosA




=4tanA * sinA.





$lhs \: = \: rhs \:$