Question

We can write ( sin a ) ^ 2 = sin ^ 2 a , but why can't we write ( sin a ) ^ -1 as sin ^ -1 a.

Answer 1

Bcoz in sin^-1(a) , -1 is not the power but rather used as inverse
Hence {sin(a)}^-1 cant be written as sin^-1(a)

Answer 2

HERE IS THE REASON;

◆ If we write

$\sin(a) {}^{ - 1} as \sin {}^{ - 1} a \: will \: be \: considered \: as \: wrong \: as \: the \: new \: result \: will \: come \: \ \frac{1}{ \sin} a$

◆ The a will not come in fraction with Sin. That's considered as wrong.

HOPE IT HELPS