What is the value of (cos(60))(sec(60)) ?

The value of (cos(60))(sec(60)) is 1

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(cos(60))(sec(60))

(cos (6 0^{\circ})) (sec (6 0^{\circ}))

1

Solution steps

(cos (6 0^{\circ})) (sec (6 0^{\circ}))

= cos (6 0^{\circ}) sec (6 0^{\circ})

Use the following trivial identity:

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

cos (6 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 0^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

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

Simplify

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

\frac{1}{2} \cdot 2

Convert element to fraction:

2 = \frac{2}{1}

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

Cross-cancel:

2

= 1

= 1

cos (0) \cdot 7

tan (10 π)

cos^{2} (3 0^{\circ}) + sin^{2} (3 0^{\circ}) - 2 cos (9 0^{\circ})

110 cos (4 8^{\circ}) (1.25)

6 cos (1)