a The first two terms of an arithmetic progression are 1 and cos 2 x respectively Show that the sum of the first ten terms can be expressed in the form a b sin 2 x, where a and b are constants to be found b The first two terms of a geometric progression are 1 and 1 3 tan 2 respectively, where i Fin...

aThe nth term of an arithmetic progression with first term a and common difference d can be calculated as follows tn a n1d The first term in this case is 1 and the second term is cos 2x So far we have ...

a. The first two terms of an arithmetic progression are 1 and cos 2 x respectively. Show

Question:

a. The first two terms of an arithmetic progression are 1 and cos²x respectively. Show that the sum of the first ten terms can be expressed in the form a − b sin²x, where a and b are constants to be found.
b. The first two terms of a geometric progression are 1 and 1/3 tan²θ respectively, where i. Find the set of values of for which the progression is convergent.
ii. Find the exact value of the sum to infinity when