Question

​If x = sec(theta) + tan(theta) and y = cosec(theta) - cot(theta) , then prove that ​y(x+1)=x-1

Answer 1

Answer:

x=sec theta + tan theta,

y=cosec theta -cot theta

to proof : y(x+1)=x-1

PROOF :

by L. H. S.

y(x+1)

=cosec theta - cot theta ( sec theta + tan theta + 1)

=cosex theta sec theta + cosec theta tan theta + codex theta - cot theta sec theta -cot theta tan theta -cot theta

= cosec theta sec theta+ sec theta+cosec theta + cosec theta - 1- cot theta

= sec theta (cosec theta +1) +2 cosec theta - cot theta -1

by R. H. S.

X-1

= sec theta + tan theta -1

hence, L. H. S. IS NOT EQUAL TO R. H. S.

y (x+1) is not equal to x-1

(from my observation they are not equal)

hope it's clear........