Question

Tan theta/(1-cot theta) + cotton theta/(1-tan theta) =(1+sec theta . Cosec theta)

Answer 1

Step-by-step explanation:

tanx/(1-cotx) + cotx/(1-tanx)

=(1+secx.cosecx)

L.H.S = tanx/(1-cotx) +cotx/(1-tanx)

:- tanx = sinx/cosx

:-cotx = cosx/sinx

(sinx/cosx)/(sinx-cosx)/sinx +

(cosx/sinx)/(cosx-sinx)/cosx

sin²x/cosx(sinx-cosx) -cos²x/sinx(sinx-cosx)

(sin³x-cos³x)/sinxcosx (sinx-cosx)

:- (a³-b³)=(a-b)(a²+ab+b²)

{(sinx-cosx)(sin²x+sinxcosx+cos²x)/sinx(sinx-cosx)

:- sin²x+cos²x =1

(1+sinxcosx)/sinxcosx

1/sinxcosx +sinxcosx/sinxcosx

1 + secx.cosecx proved

hope it helps thanku