1.

If `a^2+2a+cosec^2(pi/2(a+x))=0`, then, find the values of a and x.

Answer» Correct Answer - `a = - 1 and x=2n, n in Z`
We have `(a+1)^2+cosec^2(pi/2(a+x))-1=0`
`or (a+1)^2+cot^2(pi/2(a+x))=0`
`rArr a=-1" and " cot^2((-pi)/2+(pix)/2)=0`
`rArr tan^2((pix)/2)=0or tan((pix)/2)=0`
`rArr (pix)/2=npi,n in Z`
`rArr x=2n, n in Z`


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