Question

tantheta/1-cottheta+cottheta/1-tantheta=1+sectheta×cosectheta

Answer 1

its very easy

first convert L.H.S into sinQ and cosQ

L.H.S ==> SINQ/COSQ  DIVIDING BY 1 - COSQ/SINQ      +   COSQ/SINQ

DIVIDING BY 1 - SINQ / COS Q

===>  SINQ/COSQ * SINQ/SINQ-COSQ   +  COSQ/SINQ * COSQ / COSQ - SINQ

===>  SIN SQUARE Q / COS [ SINQ-COSQ] + COS SQUARE Q / SINQ[SINQ - COSQ]  

BY LCM

====> SIN CUBE Q - COS CUBE Q \ COS*SINQ[SINQ-COSQ]

BY using :- A cube + b cube formula

[sinQ - cosQ] [sin square Q + sinQ*cosQ + cos square Q] / cos*sin [ sin - cos]

===> we get :- 1+sincos/cos*sin   BY CUTTING

==> NOW , SEPERATE THEM

1/SINQ*COSQ + SINQ*COSQ/ COSQ*SINQ

===> SECQ*COSQ +1

===>  1+SECQ*COSQ = R.H.S

I HOPE YOU UNDERSTAND