What is the value of cot(60)tan(30)+sec^2(45)sin(30) ?

The value of cot(60)tan(30)+sec^2(45)sin(30) is 4/3

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cot(60)tan(30)+sec^2(45)sin(30)

cot (6 0^{\circ}) tan (3 0^{\circ}) + sec^{2} (4 5^{\circ}) sin (3 0^{\circ})

\frac{4}{3}

Solution steps

cot (6 0^{\circ}) tan (3 0^{\circ}) + sec^{2} (4 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

cot (6 0^{\circ}) = \frac{3}{3}

Use the following trivial identity:

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

Use the following trivial identity:

sec (4 5^{\circ}) = 2

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= \frac{3}{3} \cdot \frac{3}{3} + (2)^{2} \frac{1}{2}

Simplify

\frac{3}{3} \cdot \frac{3}{3} + (2)^{2} \frac{1}{2} : \frac{4}{3}

= \frac{4}{3}

(1)^{2} \cdot sin (\frac{π}{3}) \cdot cos (\frac{π}{3})

\frac{π}{2} [sin (0) + sin (π)]

cos (arctan (\frac{5}{4}))

csc (- 39 0^{\circ})

2 (cos (9 0^{\circ}) + i sin (9 0^{\circ}))

What is the value of cot(60)tan(30)+sec^2(45)sin(30) ?
The value of cot(60)tan(30)+sec^2(45)sin(30) is 4/3