What does $-sin(arccos(2))+tan("arccsc"(4))$ equal?

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Answer 1 · 2018-06-14T14:00:59

$-sin(arccos(2))+tan("arccsc"(4))=1/15sqrt15-sqrt3i$

We use the following identities to evaluate the above expression:

$sinx=sqrt(1-cos^2x)$

$cotx=sqrt(csc^2x-1)$

$tanx=1/cotx$

So

$-sin(arccos(2))+tan("arccsc"(4))$

$=-sqrt(1-cos^2(arccos2))+1/sqrt(csc^2("arccsc"4)-1)$

$=-sqrt(1-4)+1/sqrt(16-1)$

$-sqrt(-3)+1/sqrt15$

$=1/15sqrt15-sqrt3i$

What does -sin(arccos(2))+tan("arccsc"(4))-sin(arccos(2))+tan("arccsc"(4)) equal?