cotx cot2x - cot2x cot3x-cot3x cotx=1

What is assumed mean &how can we find it

Prove that 1.2 + 2.3 + 3.4 +..............n(n+1) = 1/3 n (n+1)(n+2)

sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)

 In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?

cos²x + cos²(x + pi/3) + cos²(x - pi/3) = 3/2. prove

prove that cos20 cos 40 cos 60 cos 80=1/16.

the second, third and fourth term of the binomial expansion (x+a)n  (n is actually (x+a)raised to the power n) are 240, 720 and 1080. find x, a and n.

Find the term independent of x in the expansion of (2x - 1/x)¹⁰

 prove that (A-B) U (B-A) =(A U B) - (A intersection B)

prove that

cosA +cosB +cosC +cos(A+B+C) = 4cos((A+B) / 2)cos((B+C) / 2)cos((C+A) / 2)

derivative using first principle -

sin_/x (sin under root x)

Differentiate sinx/x from the first principle.

sin⁴x+cos⁴x=1-2sin²xcos²x

derivative of 1)logx by first principle