What is the value of 2sec^2(45)sec(30)-3cos(60)tan(60) ?

The value of 2sec^2(45)sec(30)-3cos(60)tan(60) is (7sqrt(3))/6

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2sec^2(45)sec(30)-3cos(60)tan(60)

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

\frac{7 3}{6}

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

tan (6 0^{\circ}) = 3

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

Simplify

2 (2)^{2} \frac{2 3}{3} - 3 \cdot \frac{1}{2} 3 : \frac{7 3}{6}

= \frac{7 3}{6}

\frac{1}{arctan ( \frac{3}{4} )}

sin^{2} (4 5^{\circ}) + 8 cos^{2} (3 0^{\circ})

cos (0.6593)

tan (3 0^{\circ}) tan (6 0^{\circ})

sin (\frac{π}{4} + \frac{π}{4})

What is the value of 2sec^2(45)sec(30)-3cos(60)tan(60) ?
The value of 2sec^2(45)sec(30)-3cos(60)tan(60) is (7sqrt(3))/6