Question

how to answer this question
please solve this problem

Answer 1

LHS = ( tanA + sinA )/(tanA - sinA )

Multiply numerator and denominator

with cotA

=[CotA(tanA+sinA )]/[cotA(tanA-sinA)]

= (CotAtanA+cotAsinA)/(cotAtanA-

cotAsinA )

= [ 1 + ( cosA/sinA)sinA]/[ 1-

(cosA/sinA)sinA ]

[ Since cotA tanA = 1 ]

= ( 1 + cosA ) / ( 1 - cos A )

= ( 1 + 1/ secA ) ( 1 - 1/ secA )

=[ ( SecA + 1 ) /secA ]/[(secA-1)/secA]

= ( SecA + 1 ) / ( secA - 1 )

= RHS

Answer 2

Hey friend,  sin /cos +sin the whole divided by sin/cos-sin gives,  sin+sin*cos /cos the whole divided by sin -sin*cos /cos,  Taking sin theta common from both numerator and denominator which gives,  sin(1+cos) /cos the whole divided by sin(1-cos) /cos,  1/cos+ cos/cos the whole divided by 1/cos - cos/cos  =sec+1 /sec-1 = RHS.. (Proved)  Hope this will help you.