If, Tan a = 1/2, x = ??? My result is: x= sen a + (3/sen a) it's ok?

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1 Answer
Mar 20, 2018

The answer is #x=22/5#

Explanation:

Reminder,

#sin(a+b)=sinacosb+sinbcosa#

#cos(a+b)=cosacosb-sinasinb#

We are given

#tanalpha=1/2#

Therefore,

#sinalpha=1/sqrt5#

#cosalpha=2/sqrt5#

#tan(90-alpha)=cotalpha=2#

#sec(90-alpha)=sqrt5#

#cosec(90+alpha)=1/sin(90+alpha)#

#=1/(sin90cosalpha+sinalphacos90)#

#=1/(2/sqrt5+0)#

#=sqrt5/2#

#sin(90-alpha)=2/sqrt5#

#cos(90+alpha)=cos90cosalpha-sin90sinalpha=0-1/sqrt5#

Putting all the results together

#x=(2*sqrt5)/(sqrt5/2)-2/sqrt5*(-1/sqrt5)#

#=4+2/5#

#=22/5#