Question

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

Answer 1

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

Explanation:

`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,...}`