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If Pn=cosnx...

Question

If $P_{n} = c o s^{n} x + s i n^{n} x,$ then $2 P_{6} - 3 P_{4} + 1 =$

A

2

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B

3

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C

0

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D

1

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Solution

The correct option is C $0$
$2 P_{6} - 3 P_{4} + 1$ $= 2 (1 - 3 s i n^{2} x c o s^{2} x)$ $- 3 [(s i n^{2} x + c o s^{2} x)^{2} - 2 s i n^{2} x c o s^{2} x] + 1$
$= 2 - 6 s i n^{2} x c o s^{2} x - 3 (1 - 2 s i n^{2} x c o s^{2} x) + 1 = 0$

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