kaguirre205426 kaguirre205426
  • 12-11-2020
  • Mathematics
contestada

(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ

Respuesta :

Hrishii
Hrishii Hrishii
  • 12-11-2020

Answer:

See below

Step-by-step explanation:

[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]

Thus proved

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