Question

Find the value of tan 13π^c/12


$\frac{12}{12}$
​

Answer 1

Answer:

HI MATE.

By the tangent subtraction formula:

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

Thus:

tan(13π/12)

= tan(4π/3 - π/4), from the hint

= [tan(4π/3) - tan(π/4)]/[1 + tan(4π/3)tan(π/4)], from the above formula

= (-1 + √3)/(1 + √3)

= -(1 - √3)/(1 + √3)

= -(1 - √3)^2/[(1 + √3)(1 - √3)], by rationalizing

= -(1 - √3)^2/(1 - 3), via difference of squares

= (1/2)(1 - √3)^2

= (1/2)(1 - 2√3 + 3)

= (1/2)(4 - 2√3)

= 2 - √3.

Hope it helps you mate.

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Answer 2

See the attached photo

Hope it helps you