How do you simplify $sin(cos^-1(2/3)-sin^-1(2/3))$ ?

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Answer 1 · 2016-07-29T17:37:48

$1/9$

Use $sin^(-1)x+cos^(-1)x=pi/2$ . Here, $x = 2/3$ .

Let $cos^(-1)(2/3)=a$ . Then $cos a = 2/3$ .

Now, the given expression is

$sin(2a-pi/2)$

$=-cos 2a$

$=1-2cos^2a$

$=(1-8/9)$

$=1/9$

How do you simplify sin(cos^-1(2/3)-sin^-1(2/3))sin(cos^-1(2/3)-sin^-1(2/3))?