Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression.?
(1+cot x)(1-tan x)
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(1+cot x)(1-tan x)
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( 1 + cosx/sinx ) ( 1 - sinx/cosx )
1 - sinx/cosx + cosx/sinx - 1
- sin²x + cos²x
----------------------- = - tan x + cot x
sin x cos x
(1+cot x)(1-tan x)
= (1 + cos x/sin x)(1 - sin x/cos x)
= (sin x + cos x)(cos x - sin x)/(sin x cos x)
= (cos²x - sin²x)/(sin x cos x)
= 2cos(2x)/sin(2x)
= 2cot(2x)