Question

please solve this question as fast as you can

Answer 1

Hiii friend,

Tan theta/1 - Cot theta + Cot theta/1-Tan theta = 1 + Tan theta+Cot theta

We have,

LHS = Tan theta/1-Cot theta + Cot theta/1-Tan theta

=> Sin¢/Cos¢ + Cos¢/Sin¢
__________**_________
(1-Cos¢/Sin¢ *** (1-Sin¢/Cos¢

=> (Sin²theta)/Cos theta (Sin theta-Cos theta) + Cos²theta/Sin theta (Cos theta-Sin theta)

=> Sin²theta/Cos theta (Sin theta-Cos theta) - Cos²theta/Sin theta (Sin theta-Cos theta)

=> Sin³theta - Cos³theta/Sin²theta Cos²theta (Sin theta-Cos theta)

=> (Sin theta-Cos theta)(Sin²theta+Cos²theta+SinA CosA)/Sin theta Cos theta (Sin theta - Cos theta) [ (A³-B³) = (A-B)(A²+B²+AB]

=> 1+Sin theta × Cos theta/Sin theta× Cos theta

And,

RHS = (1+Tan theta+Cot theta)

=> ( 1 + Sin theta/Cos theta + Cos theta/ Sin theta)

=> Sin theta × Cos theta + Sin²theta+Cos²theta/Sin theta Cos theta

=> (1+Sin theta Cos theta)/(Sin theta Cos theta)

Hence,

LHS = RHS.

HOPE IT WILL HELP YOU........ :-)