Question

QUESTION NO. V, PLS ANSWER FAST ⏩

Answer 1

$Hey$

Mate here's the Solution.....

Cos A - SinA + 1 / Cos A + Sin A - 1 = Cosec A + Cot A


L.H.S.



CosA-sinA+1/cosA+sinA-1

=(cosA-sinA+1)(cosA+sinA+1)/(cosA+sinA-1)

(cosA+sinA+1)

=(cos²A-cosAsinA+cosA+cosAsinA-

sin²A+sinA+cosA-sinA+1)/{(cosA+sinA)²-(1)²}


=(cos²A-sin²A+2cosA+1)/

(cos²A+2cosAsinA+sin²A-1)


={cos²A+2cosA+(1-sin²A)}/(1+2cosAsinA-1)

[∵, sin²A+cos²A=1]



=(cos²A+2cosA+cos²A)/2cosAsinA


=(2cos²A+2cosA)/2cosAsinA


=2cosA(cosA+1)/2cosAsinA



=(cosA+1)/sinA


=cosA/sinA+1/sinA


=cotA+cosecA


=cosecA+cotA (Proved)