How do you solve $sec (2gamma +10)= csc(4gamma)$ ?

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Answer 1 · 2016-06-22T19:53:44

$gamma = pi/12-10/6+pi/3 k,$ ${k = 0, pm1,pm2,pm3,...}$

$sec (2gamma +10)= csc(4gamma)->cos(2gamma+10)=sin(4gamma)$

but

$cos(2gamma+10)=sin(4gamma)=cos(pi/2-4gamma)$

we conclude

$2 gamma + 10 = pi/2-4gamma + 2k pi$

$gamma = pi/12-10/6+pi/3 k,$ ${k = 0, pm1,pm2,pm3,...}$

How do you solve sec (2gamma +10)= csc(4gamma)sec (2gamma +10)= csc(4gamma)?