What is the value of 3tan(45)+csc(30)cos(60) ?

The value of 3tan(45)+csc(30)cos(60) is 4

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3tan(45)+csc(30)cos(60)

3 tan (4 5^{\circ}) + csc (3 0^{\circ}) cos (6 0^{\circ})

4

Solution steps

3 tan (4 5^{\circ}) + csc (3 0^{\circ}) cos (6 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

csc (3 0^{\circ}) = 2

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

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

Simplify

3 \cdot 1 + 2 \cdot \frac{1}{2} : 4

= 4

\frac{sin ( 4 7 ^{\circ} ) + cos ( 1 7 ^{\circ} )}{cos ( 4 7 ^{\circ} ) + sin ( 1 7 ^{\circ} )}

10 cos (7 5^{\circ}) cos (1 5^{\circ})

cos^{2} (\frac{5 π}{6}) - 2 sin (\frac{5 π}{6})

- sin (27 0^{\circ})

arcsin (sin (- \frac{7 π}{4}))

What is the value of 3tan(45)+csc(30)cos(60) ?
The value of 3tan(45)+csc(30)cos(60) is 4