Simplify : (sin pi/3)^2 +(cot pi/6)^2 +(sec pi/4)^2Can someone show me the steps to solving this?

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Simplify `(sin (pi/3))^2+(cot (pi/6))^2+(sec (pi/4))^2` :

`sin (pi/3)=sqrt(3)/2`

`cot (pi/6) = sqrt(3)`

`sec(pi/4)=2/sqrt(2)`

so the sum is

`(sqrt(3)/2)^2+(sqrt(3))^2+(2/sqrt(2))^2=3/4+3+2=5.75`

Note that `cot x =1/(tan x)` and `secx = 1/cosx`

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