sin cos tan 75?

Grade:10

2 Answers

Ganga sagar Kothashiv
32 Points
11 years ago

(31/2+1)/(2*21/2)

(31/2-1)/(2*21/2)

(31/2+1)/(31/2-1)

Aman Bansal
592 Points
11 years ago

Dear Balsingh,

sin(75)=sin(45+30)
=sin45cos30+sin30cos45
=sqrt(2)/2*sqrt(3)/2+1/2*sqrt(2)/2
factor out a sqrt(2) and the 1/4 and you get
Sin75° = √2/4(1+√3)

cos(75)=cos(45+30)
=cos45cos30-sin45sin30
=sqrt(2)/2*sqrt(3)/2-sqrt(2)/2*1/2
factor out a sqrt(2) and the 1/4 and you get
Cos75° = √2/4(√3-1)

tan75=sin75/cos75
=√2/4(1+√3)/√2/4(√3-1)
the √2/4 goes away
so it''s (1+√3)/(√3-1)
rationalize the denominator by multiplying (1+√3) on the top and bottom
you get (1+√3)^2/2 after simplifying
=(1+2√3+3)/2
=√3 +2

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