What is the value of (tan(45)+tan(60))^2 ?

The value of (tan(45)+tan(60))^2 is 4+2sqrt(3)

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(tan(45)+tan(60))^2

(tan (4 5^{\circ}) + tan (6 0^{\circ}))^{2}

4 + 23

Solution steps

(tan (4 5^{\circ}) + tan (6 0^{\circ}))^{2}

Use the following trivial identity:

tan (4 5^{\circ}) = 1

Use the following trivial identity:

tan (6 0^{\circ}) = 3

= (1 + 3)^{2}

Simplify

(1 + 3)^{2} : 4 + 23

= 4 + 23

sin^{3} (\frac{2 π}{3})

(2 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4})))^{3}

cos (4 5^{\circ}) 8

cos (23 4^{\circ})

sin (4) (\frac{π}{6})

What is the value of (tan(45)+tan(60))^2 ?
The value of (tan(45)+tan(60))^2 is 4+2sqrt(3)