Question

prove that 2- 3sinalpha- sin³alpha/sinalpha+2=2sinalpha(sinalpha-1)+ cos²alpha​

Answer 1

Answer:

Let 3sinα−2cosα=t ...(1)

Given : 2sinα+3cosα=2 ...(2)

⟹(3sinα−2cosα)

2

+(2sinα+3cosα)

2

=t

2

+2

2

⟹9sin

2

α−12sinαcosα+4cos

2

α+4sin

2

α+12sinαcosα+9cos

2

α=t

2

+4

⟹13(sin

2

α+cos

2

α)=t

2

+4

⟹ t

2

=9

⟹

t=±3

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