What does $cos(arctan(2))-sin(arcsec(5))$ equal?

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Answer 1 · 2016-05-19T10:04:26

$cos(arctan2)-sin(arcsec5)$ is $+-1.427$ or $+-0.5326$

$cos(arctan2)-sin(arcsec5)$

= $cosalpha-sinbeta$ , where

$tanalpha=2$ and $secbeta=5$

Now, $cosalpha=i/secalpha=1/sqrt(1+tan^2alpha)$

= $1/sqrt(1+2^2)=+-1/sqrt5$

and $sinbeta=sqrt(1-cos^2beta)=sqrt(1-1/sec^2beta)$

= $sqrt(1-1/5^2)=sqrt(1-1/25)=sqrt(24/25)=+-2/5sqrt6$

Hence $cosalpha-sinbeta=(+-1/sqrt5)-(+-2/5sqrt6)$

= $(+-0.4472)-(+-0.9798)$

Taking different sign combinations can take four different values of $cosalpha-sinbeta$ , which are $+-1.427$ or $+-0.5326$

What does cos(arctan(2))-sin(arcsec(5))cos(arctan(2))-sin(arcsec(5)) equal?