Question

prove 1-cosA/1+cosA=(cosecA-cotA)²


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Answer 1

1-cosA/1+cosA=(cosecA-cotA)²

LHS = 1-cosA/1+cosA

(Divide Numerator and Denominator by sinA)

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

LHS = (cosecA - cotA)/(cosecA + cotA)

(Multiply Numerator and Denominator by (cosecA - cotA) )

LHS = [(cosecA - cotA)/(cosecA + cotA)] x [(cosecA - cotA)/(cosecA - cotA)]

[(cosecA + cotA)(cosecA - cotA) = cosec^2A - cot^2A]

LHS = (cosecA - cotA)^2/(cosec^2A - cot^2A)

(cosec^2A - cot^2A = 1)

LHS = (cosecA - cotA)^2/ 1

LHS = (cosecA - cotA)^2

LHS = RHS

Hence, Proved

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