What does $4 csc (a r c cot (7)) - 2 cos (arctan (5))$ $4csc(arc cot(7))-2cos(arctan(5))$ equal?

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Answer 1 · 2018-04-08T16:45:31

$4 csc (a r c cot (7)) - 2 cos (arctan (5)) = 20 \sqrt{2} - \frac{2}{\sqrt{26}}$ $4csc(arc cot(7))-2cos(arctan(5))=20sqrt2-2/sqrt26$

Let $a r c cot 7 = A$ $arc cot7=A$ then $cot A = 7$ $cotA=7$

and $csc A = \sqrt{1 + 7^{2}} = \sqrt{50} = 5 \sqrt{2}$ $cscA=sqrt(1+7^2)=sqrt50=5sqrt2$

Hence $4 csc (a r c cot (7)) = 4 \cdot 5 \sqrt{2} = 20 \sqrt{2}$ $4csc(arc cot(7))=4*5sqrt2=20sqrt2$

Let $arctan 5 = B$ $arctan5=B$ then $tan B = 5$ $tanB=5$ and

$cos B = \frac{1}{sec B} = \frac{1}{\sqrt{1 + 5^{2}}} = \frac{1}{\sqrt{26}}$ $cosB=1/secB=1/sqrt(1+5^2)=1/sqrt26$

and $2 cos (arctan (5)) = \frac{2}{\sqrt{26}}$ $2cos(arctan(5))=2/sqrt26$

i.e. $4 csc (a r c cot (7)) - 2 cos (arctan (5)) = 20 \sqrt{2} - \frac{2}{\sqrt{26}}$ $4csc(arc cot(7))-2cos(arctan(5))=20sqrt2-2/sqrt26$

What does 4csc(arccot(7))−2cos(arctan(5))4csc(arc cot(7))-2cos(arctan(5)) equal?