Prove
that.
(Cos2A+Sin2A) /(Cos2A-Sin2A) =(1-Sin2A) /Cos2A
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Secondary SchoolMath 13 points
Prove :SIN2A/COS2A+COS2A/SIN2A= 1/SIN2A.COS2A -2
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Answer:
Proved
Step-by-step explanation:
prove :SIN2A/COS2A+COS2A/SIN2A= 1/SIN2A.COS2A -2
Question is
\frac{Sin^2A}{Cos^2A} + \frac{Cos^2A}{Sin^2A} = \frac{1}{Sin^2A Cos^2A} - 2
LHS = \frac{Sin^2A}{Cos^2A} + \frac{Cos^2A}{Sin^2A}
= = \frac{Sin^4A + Cos^4A}{Cos^2A . Sin^2A}\\\\Using\: a^2 + b^2 = (a+b)^2 - 2ab\\\\a = Cos^2A \: \& \:b = Sin^2A\\\\= \frac{(Sin^2A + Cos^2A)^2 - 2Sin^2A Cos^2A}{Cos^2A Sin^2A} \\\\Sin^2A + Cos^2A = 1\\\\= \frac{1 -2Sin^2A Cos^2A}{Cos^2A Sin^2A}
= \frac{1}{Cos^2A Sin^2A} - 2\\\\= RHS
QED