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Trigonometric identities.. what is the solution why -sinx = (cot x - csc x)(cos x +1) ?

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by jammmal

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by jammmal

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=( cos x/sin x - 1/sin x)(cos x + 1) / cot x = cos x/sin x; csc x = 1/sin x

=( cos x-1)/sin x)(cos x+ 1)

= (cos² x-1)/sin x / ( cos x-1)(cos x+1) = cos² -1

= - sin² x/sin x / sin² x + cos² x = 1 or cos² x -1 = -sin² x

= -sin x

so (cot x - csc x)(cos x+ 1) = -sin x

I'm not actually sure with my answer since we were only taught the basics in trigonometry but I still hope this helps.