Question

The value of tan75° is​

Answer 1

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Let us write 75 degrees as a sum of two angles 45 degrees and 30 degrees.

We have written 75 degrees as a sum of two angles so that we can use the trigonometric formula.

tan (x+y) = (tanx + tany) / (1 - tan x tan y)

On substituting the value of x as 45 degree and y as 30 degree, we get,

tan (45°+30°) = (tan45°+ tan30°) / (1-tan45° tan30°)

= {1+ (1/√3)} / {1-(1/√3)}

Therefore, tan75° = (√3 + 1) / (√3 - 1)

Answer 2

Answer:

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Step-by-step explanation:

so here tan 75 can be written as tan(45+30)

so here tan(45+30) is in form tan(A+B)

so we know that

tan(A+B)=tan A+tan B/1-tan A.tan B

so here A=45 and B=30

thus then

=tan 45+tan 30/1-tan 45.tan 30

so we know that

tan 45=1

tan 30=1/√3

thus then

=1+1/√3/1-1×1×1/√3

=√3+1/√3/1-1/√3

=√3+1/√3/√3-1/√3

=√3+1/√3-1

so we know that

√3=1.73

ie 1.73+1/1.73-1

=2.73/0.73

=3.7397

=3.73

hence tan 75=√3+1/√3/√3-1/√3 ie 3.73