Write the difference in tanpi/4-cosx as a product?  

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We have to write tan ( pi/4) - cos x as a product

We know that tan x = sin x / cos x and tan (pi/4) = 1

tan ( pi/4) - cos x

=> 1 - cos x

we can write 1 as cos 0

=> cos 0 - cos x

=> −2 sin ( 0 + x)/2 * sin (0 - x)/2

=> -2* sin x/2 * sin -x/2

=> 2* sin x/2 * sin x/2

=> 2* (sin x/2)^2

Therefore the required result is 2* (sin x/2)^2

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