What is the value of tan(30)cot(30)+cos(360)sin(150) ?

The value of tan(30)cot(30)+cos(360)sin(150) is 3/2

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tan(30)cot(30)+cos(360)sin(150)

tan (3 0^{\circ}) cot (3 0^{\circ}) + cos (36 0^{\circ}) sin (15 0^{\circ})

\frac{3}{2}

Solution steps

tan (3 0^{\circ}) cot (3 0^{\circ}) + cos (36 0^{\circ}) sin (15 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cot (3 0^{\circ}) = 3

Rewrite using trig identities:

cos (36 0^{\circ}) = 1

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

= \frac{3}{3} 3 + 1 \cdot \frac{1}{2}

Simplify

\frac{3}{3} 3 + 1 \cdot \frac{1}{2} : \frac{3}{2}

= \frac{3}{2}

\frac{2 cos ^{2} ( 4 5 ^{\circ} ) - 1}{tan ( 4 5 ^{\circ} )}

40 \cdot cos (2 0^{\circ})

sin (4 5^{\circ}) 3

2 sin (\frac{π}{2})

tan (3.5)

What is the value of tan(30)cot(30)+cos(360)sin(150) ?
The value of tan(30)cot(30)+cos(360)sin(150) is 3/2