What does $sin (a r c tan (2)) + 3 cot (arctan (- 1))$ $sin(arc tan(2))+3cot(arctan(-1))$ equal?

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What does $sin (a r c tan (2)) + 3 cot (arctan (- 1))$ $sin(arc tan(2))+3cot(arctan(-1))$ equal?

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Answer 1 · 2016-03-22T15:18:59

$\frac{2}{\sqrt{5}} - 3$ $2/sqrt5-3$

Explanation:

If $tan A = \frac{2}{1}, sin A = \frac{2}{\sqrt{2^{2} + 1^{2}}} = \frac{2}{\sqrt{5}}$ $tan A = 2/1, sin A = 2/sqrt(2^2+1^2)=2/sqrt5$ /
If tan B = $- 1, cot B = \frac{1}{- 1} = - 1$ $-1, cot B = 1/(-1)=-1$ .
$sin (a r c tan (2)) + 3 cot (a r c tan (- 1))$ $sin(arc tan(2)) + 3 cot (arc tan (-1))$
= $sin (a r c sin (\frac{2}{\sqrt{5}})) + 3 cot (a r c cot (- 1))$ $sin(arc sin(2/sqrt5)) + 3 cot (arc cot (-1) )$
= $\frac{2}{\sqrt{5}} + 3 (- 1) = \frac{2}{\sqrt{5}} - 3$ $2/sqrt5+3(-1)= 2/sqrt5-3$

IF $O^{- 1}$ $O^(-1)$ is the inverse of the operator O,
$O (O^{- 1}) \equiv O^{- 1} (O) \equiv 1$ $O(O^(-1))-=O^(-1)(O) -= 1$ -

Examples: sin (arc sin x ) = x and $a^{{log}_{a} x}$ $a^(log_a x)$ = x.

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What does $sin (a r c tan (2)) + 3 cot (arctan (- 1))$ $sin(arc tan(2))+3cot(arctan(-1))$ equal?

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What does $sin (a r c tan (2)) + 3 cot (arctan (- 1))$ $sin(arc tan(2))+3cot(arctan(-1))$ equal?