Question 962295
I do not think you need to use identities to solve this

{{{ sin ( pi/6 ) + tan^2 ( pi/5 )}}}

since {{{ sin ( pi/6 )=1/2}}}, and

{{{tan^2 ( pi/5 )=tan ( pi/5 )*tan( pi/5 )}}}, and

{{{tan ( pi/5 )=sqrt(5-2 sqrt(5))}}} then

{{{tan^2 ( pi/5 )=(sqrt(5-2sqrt(5)))^2}}}

{{{tan^2 ( pi/5 )=5-2sqrt(5)}}}

so we have:

{{{ 1/2 + (5-2sqrt(5))}}}

{{{ 1/2 + 10/2-2sqrt(5))}}}

{{{ 11/2-2sqrt(5))}}}

the exact value of the expression is:{{{11/2-2sqrt(5)}}}