Question

prove tan theta+sin theta/tan theta-sin theta =sec theta+1/sec theta-1

Answer 1

Hi ,

Here I used A instead of theta,

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

I hope this helps you.

:)

Answer 2

Answer:

HS = ( 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

I hope this helps you.

:)

Step-by-step explanation: