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il63 [147K]
3 years ago
6

(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ

Mathematics
1 answer:
ohaa [14]3 years ago
8 0

Answer:

See below

Step-by-step explanation:

( \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

Thus proved

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