n=1n2_ 4 9 16 _6 1. Verify the following trigonometric identity. (So long as :L' is not an integer multiple of 71' anyway!-) [2] 1 _ 1 1 + 1...

only question number 2.Verify the following trigonometric summation formula for m ≥ 1.

Your task on this assignment will be to show that: n=1n2_ 4 9 16 _6 1. Verify the following trigonometric identity. (So long as :L‘ is not an integer multiple of71' anyway! :-) [2] 1 _ 1 1 + 1sin2(ac) _ 4 sin2 g) sin2 (%)Hint: Use common trig identities and the fact that for any t, cos(t) = sin (t + g). 2. Verify the following trigonometric summation formula for m 2 1. [2] 2m—1m1 2 11 = 4—771 2 - 2 £2k+llfl19:0 3111 ( 2m+l ). . . . . 1Hmt: Apply the 1dent1ty from question 1 repeatedly, starting from 1 = Tm. You8111 —2 may find the fact that sin(t) = sin(7r — t) comes in handy.3. Verify the following limit formula, where k 2 0 is fixed. [2] (2k + 1)7r _ (2k + 1)7r21’1“"1 2 lim 2m sin ( — TIL—>00 Hint: This is really just (a version of) limtno %fl = 0 . . .