Question

prove that 6(cos^10 x+ sin^10x) - 15(cos^8x + sin^8x) + 10(cos^6x + sin^6x)=1

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Tn=sin^n+cos^n = s^n+c^n

Tn - Tn-2 = s^n+c^n-(s^n-2 - c^n-2)

               = s^n - s^n-2 +c^n - c^n-2

               = -s^n-2(1-s^2) -c^n-2(1-c^2)

               = -s^n-2(c^2) - c^n-2(s^2)

               = -c^2s^2(s^n-4 + c^n-4)

Tn - Tn-2 = -c^2s^2(Tn-4)  Let c^2s^ = x

               = -xTn-4

When n=4

T4                     = 1-2x

When n=6

T6                     = 1-3x

When n=8

T8           = 2x^2-4x+1

When n=10

T10              = 5x^2-5x+1

Now 

=6(sin^10+cos^10) - 15(sin^8+cos^8) +10(sin^6+cos^6) = 6.T10 - 15T8 + 10.T6

=6(5x^2-5x+1) - 15(2x^2-4x+1) + 10(1-3x)

=30x^2-30x+6-30x^2+60x-15+10-30x

=6+10-15

=1.