sinΦ.tanΦ/1-cosΦ=1+secΦ
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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
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
sdklvkb:
thanks
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