How do you simplify $cos(sin^-1(3/5)-cos^-1(1/2))$ ?

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Answer 1 · 2016-05-13T04:41:14

$(1/10)(+-4+-3sqrt3)$

Let $a = sin^(-1)(3/5) and b = cos ^(-1)(1/2)$ .

Then, $sin a = 3/5, cos a = +-4/5, cos b = 1/2 and sin b = +-sqrt3 /2$

Now, the given expression is $cos (a - b )$

$= cos a cos b + sin a sinb$

$=+-2/5+-3sqrt3/10=(1/10)(+-4+-3sqrt3)$ .

The choice of sign depends on the specified ranges (if any ), for the inverse angles.a and b.

How do you simplify cos(sin^-1(3/5)-cos^-1(1/2))cos(sin^-1(3/5)-cos^-1(1/2))?