Question

Prove that
SinA/cosA+cosecA = sinA/cotA-cosecA +2
(+2 is written with whole Right hand side)

Answer 1

Answer:

Hey Mate,

LHS = $\frac{sinA}{cotA} +cosecA$

= $\frac{SinA}{(cosA/sinA+1/sinA)}$

= $\frac{SinA}{(cosA+1)/sinA}$

= $\frac{Sin^{2}A}{(1+cosA)}$

= $\frac{ (1-cos^{2}A)}{(1+cosA)}$

= $\frac{ ( 1+cosA)(1-cosA)}{(1+cosA)}$

= 1 - cosA

= 2-1-cosA

= 2 - (1 + cosA)

= $2- \frac{(1+cosA)(1-cosA)}{(1-cosA)}$

= $\frac{ (1-cos^{2}A)}{-(1-cosA)}+2$

= $\frac{ si^{2}A}{(cosA-1)}+2$

= $\frac{sinA}{(cosA-1)/sinA}+2$

= $\frac{sinA}{(cosA/sinA-1/sinA)}+2$

= $\frac{ sinA}{cotA-cosecA}+2$ = RHS