i need to prove identityi'll have to find cotangent of sum of 2 angles, before differentiating.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll write the tangent formula:

cot(a+b) = cos(a+b)/sin(a+b)

We'll prove this formula substituting the sine and cosine functions by their formulas for the sine and cosine of the sum of angles a and b:

sin(a+b) = sina*cosb + sinb*cosa

cos(a+b) = cosa*cosb - sina*sinb

We'll substitute sin(a+b) and cos(a+b) by their formulas:

cot(a+b) = (cosa*cosb - sina*sinb)/(sina*cosb + sinb*cosa)

We'll factorize by sina*sinb:

cot(a+b) = sina*sinb*[(cosa*cosb/sina*sinb) - 1]/sina*sinb*(cot b + cot a)

We'll simplify and we'll get:

cot(a+b) = (cot a*cot b - 1)/(cot b + cot a)

The formula of cotangent of the sum of 2 angles is:

cot(a+b) = (cot a*cot b - 1)/(cot b + cot a)

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