What is the value of 2sin(60)sec(30)cos(45)tan(45) ?

The value of 2sin(60)sec(30)cos(45)tan(45) is square root of 2

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2sin(60)sec(30)cos(45)tan(45)

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

2

Solution steps

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

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

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

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

Simplify

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

= 2

3 + 2 sin (\frac{π}{4})

cos (3 0^{\circ}) + tan (4 5^{\circ})

arctan (\frac{2.5}{1.8})

7 sin (4 0^{\circ})

5 tan (3 0^{\circ})

What is the value of 2sin(60)sec(30)cos(45)tan(45) ?
The value of 2sin(60)sec(30)cos(45)tan(45) is square root of 2