Find the principal value of :

(i)


(ii)


(iii)


(iv)


(v)


(vi)


(i) Let


[Formula: sin-1(-x) = -sin-1 x ]


[We know which value of x when put in this expression will give us this result]



(ii) [ Formula: cos-1(-x) = π – cos-1 x]


Let


[We know which value of x when put in this expression will give us this result]



Putting this value back in the equation



(iii) Let


[Formula: tan-1(-x) = - tan-1 (x)]


[We know which value of x when put in this expression will give us this result]



(iv) …(i) [ Formula:sec-1(-x) = π– sec-1 (x) ]


Let


[We know which value of x when put in this expression will give us this result]



Putting the value in (i)



(v) Let


[ Formula: cosec-1(-x) = -cosec-1 (x) ]




(vi) … (i)


Let


[We know which value of x when put in this expression will give us this result]



Putting in (i)



=


1