Question

sinΦ.tanΦ/1-cosΦ=1+secΦ

Answer 1

cscϕ/secϕ = (1+cotϕ)/(1+tanϕ) 


LHS = (1+cotϕ)/(1+tanϕ) 
where cotϕ=cosϕ/sinϕ and tanϕ = sinϕ/cosϕ 
= (1+(cosϕ/sinϕ))/(1+(sinϕ/cosϕ)) 
= ((cosϕ+sinϕ)/sinϕ)/((cosϕ+sinϕ)/cosϕ) 
= cosϕ/sinϕ 

wkt cosϕ=1/secϕ 
and sinϕ=1/cosecϕ 
= cscϕ/secϕ 

LHS = RHS 

hence prooved