Question

what is the short cut for finding inverse trignometric functions?

Answer 1

You do not need TRICKS. You just realise that the inverse of any function is its REFLECTION in the line y = x.

One important fact to remember is that the inverse may not be a “function” itself. If it has 2 or more points in a vertical line it is just a “relation”.

I prefer to draw a few periods of the graphs to get a better idea. You can cut them down so that the inverses are functions once you get the idea of reflecting better.

Here are graphs of y = sin(x) and the inverse y = arcsin(x) . The line is y = x
you want to leant it there is no shortcit trignometry

Answer 2

$\implies$

卄εrε αrε soмε ωαүs . . . .

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a) sin-1( x1 ) = cosec -1 x,x≥1 or x≤ -1.

b) cos-1( x1 ) = sec -1x, x≥1 or x≤-1.

c) tan -1( x1 ) = cot -1x, x>0.

a) sin-1 x+ cos-1x 2π , X∈ |-1,1|

b) tan-1 x + cot-1 x = 2π , X∈ R.

c) cosec-1 + sec-1x = 2π , |x|≥ 1.