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Question
Prove that (sin x – cos x + 1) ⋅ (sec x – tan x) = (sin x + cos x – 1).
Theorem
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Solution
LHS = (sin x – cos x + 1) ⋅ (sec x – tan x)
= `(sinx - cosx + 1).((1 - sinx)/cosx)`
= `(1 + sinx)((1 - sinx)/cosx) - cosx((1 - sinx)/cosx)`
= `((1 - sin^2x)/cosx) - (1 - sinx)`
= `(cos^2x)/(cosx) - 1 + sinx`
= sin x + cos x – 1 = RHS
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