If $sinalpha=3/5$ and $alpha$ lies in Q2 and $sinbeta=5/13$ and $beta$ lies in Q1, find $cos(alpha+beta)$ , $cosbeta$ and $tanalpha$ ?

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Answer 1 · 2017-03-16T16:16:09

$cos(alpha+beta)=-63/65$ ; $cosbeta=12/13$ and $tanalpha=-3/4$

As $sinalpha=3/5$ and $alpha$ lies in Q2, $cosalpha$ is negative and

$cosalpha=sqrt(1-sin^2alpha)=sqrt(1-(3/5)^2)$

= $sqrt(1-9/25)=sqrt(16/25)=-4/5$

and $tanalpha=sinalpha/cosalpha=(3/5)/(-4/5)=3/5xx(-5/4)=-3/4$

further as $sinbeta=5/13$ and $beta$ lies in Q1, $cosalpha$ is positive and

$cosbeta=sqrt(1-sin^2beta)=sqrt(1-(5/13)^2)$

= $=sqrt(1-25/169)sqrt(144/25)=12/13$

and $cos(alpha+beta)$

= $cosalphacosbeta-sinalphasinbeta$

= $-4/5xx12/13-3/5xx5/13$

= $-48/65-15/65=-63/65$

If sinalpha=3/5sinalpha=3/5 and alphaalpha lies in Q2 and sinbeta=5/13sinbeta=5/13 and betabeta lies in Q1, find cos(alpha+beta)cos(alpha+beta), cosbetacosbeta and tanalphatanalpha?