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Verify the identity. (sin x - cos x)(sin x + cos x) = 1 - 2 cos^(2) x

User Rosaly
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Answer:

see explanation

Explanation:

using the trigonometric identity

sin²x + cos²x = 1 ( subtract cos²x from both sides ) , so

sin²x = 1 - cos²x → (1)

consider the left side

(sinx - cosx)(sinx + cosx) ← expand using FOIL

= sin²x + sinxcosx - sinxcosx - cos²x ← collect like terms

= sin²x - cos²x ← substitute (1) from above into the expression

= (1 - cos²x) - cos²x

= 1 - cos²x - cos²x

= 1 - 2cos²x

= right side , thus verified

User Sequan
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