An arithmetic progression is a sequence of numbers that have a common difference between each term in the sequence. This means that `sin^2a-sina` , and `1-sin^2a` must be the same difference, which gives the equation:
`sin^2a-sina=1-sin^2a` where a is acute
`2sin^2a-sina-1=0` factor this
This means that either `sina=-1/2` or `sina=1` . Since a is between 0 and 90 degrees, then the first equation is not valid, so `a=pi/2` .
The value of a is `a=pi/2` .
`sin(a),sin^2(a),1 ` are in Arithmetic progression. Therefore
Let `sin^2(a)=x` ,therefore above equation reduces to
factoring by spliting middle term.
so AP will be 1,1,1
so A.P. will be -1/2,1/4,1
`a=-pi/6 or pi/2`
In above answer a=pi/2