question13,15,16,17,19

For this either base should be 1 or power should be zero
for base as zero |cosx| = 1
x should be n
Cleary at n power is not 0 which implies different roots
now sin²x -3/2 (sinx) +1/2 =0
Solve it using midle term splitting we will get sinx= 1 or sinx= ½
for sinx=1 x= /2 it wil become 0⁰ form which is indeterminate form Hence it is neglected

For sinx=1/2 x= /6 for which base will not be 0 hence it can be accepted
General solution n + (-1)ⁿ/6

Hence A is the correct answer

For other questions please post it one by one.