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Ksju [112]
3 years ago
9

1+cos2A /1-cos2A=cotA.cotA​

Mathematics
1 answer:
Allisa [31]3 years ago
6 0

Answer:

See Explanation

Step-by-step explanation:

formulae \: to \: be \: used :  \\  \cos 2 \theta = 2 { \cos}^{2}  \theta - 1 \\ and \\ \cos 2 \theta = 1 - 2 { \cos}^{2}  \theta  \\  \\ now \: let \: us \: prove \: the \: given \: trigonometrical \:  \\ identity. \\  \\  \frac{1 +  \cos2A}{1  -   \cos2A}  = \cot \: A. \cot \: A \\ LHS =  \frac{1 +  \cos2A}{1  -   \cos2A}  \\  \\  =  \frac{1 +2 { \cos}^{2}   A- 1 }{1 - (1  - 2 { \sin}^{2}   A)}  \\  \\ =  \frac{1 +2 { \cos}^{2}   A- 1 }{1 - 1   + 2 { \sin}^{2}   A}  \\  \\ =  \frac{2 { \cos}^{2}   A }{2 { \sin}^{2}   A}  \\  \\ =  \frac{{ \cos}^{2}   A }{ { \sin}^{2}   A}  \\  \\  =  { \cot}^{2} A \\  \\  =  { \cot} A .{ \cot} A \\  \\  = RHS \\  \\ hence \: proved.

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