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multiply with cos* with lhs and in rhs break sin2* by (1-cos2*)
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LHS
[tex] \frac{1+ sec (x)}{sec(x)} = \frac{1+ \frac{1}{cos(x)} }{\frac{1}{cos(x)}} \\ = \frac{cos(x)+1}{\frac{cos(x)}{cos(x)}} = cos(x)+1[/tex]
RHS
[tex] \frac{sin^2(x)}{1-cos(x)} = \frac{1-cos^2(x)}{1-cos(x)} \\ = \frac{1-cos^2(x)}{1-cos(x)} \\ = \frac{(1-cos(x))(1+cos(x))}{1-cos(x)} = 1 + cos(x)[/tex]
LHS = RHS
Hence proved
[tex] \frac{1+ sec (x)}{sec(x)} = \frac{1+ \frac{1}{cos(x)} }{\frac{1}{cos(x)}} \\ = \frac{cos(x)+1}{\frac{cos(x)}{cos(x)}} = cos(x)+1[/tex]
RHS
[tex] \frac{sin^2(x)}{1-cos(x)} = \frac{1-cos^2(x)}{1-cos(x)} \\ = \frac{1-cos^2(x)}{1-cos(x)} \\ = \frac{(1-cos(x))(1+cos(x))}{1-cos(x)} = 1 + cos(x)[/tex]
LHS = RHS
Hence proved
ritha1:
srrryyy
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