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Sin2a and Cos2a in Terms of Tana

If P n =cos n...

Question

If $P_{n} = {cos}^{n} x + {sin}^{n} x,$ then $2 P_{6} - 3 P_{4} + 1 =$

A

2

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B

3

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C

1

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Solution

$2 P_{6} - 3 P_{4} + 1 = 2 ((1 - 3 {sin}^{2} x {cos}^{2} x) - 3 [({sin}^{2} x + {cos}^{2} x)^{2} - 2 {sin}^{2} x {cos}^{2} x] + 1$
$= 2 - 6 {sin}^{2} x {cos}^{2} x - 3 (1 - 2 {sin}^{2} x {cos}^{2} x) + 1 = 0$

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Sin2a and Cos2a in Terms of Tana

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