What is the value of 3sec^2((7pi)/6) ?

The value of 3sec^2((7pi)/6) is 4

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3sec^2((7pi)/6)

3 sec^{2} (\frac{7 π}{6})

4

Solution steps

3 sec^{2} (\frac{7 π}{6})

Rewrite using trig identities:

sec^{2} (\frac{7 π}{6}) = tan^{2} (\frac{π}{6}) + 1

= 3 (tan^{2} (\frac{π}{6}) + 1)

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

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

Simplify

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

= 4

cos (33 0^{\circ}) tan (- 31 5^{\circ}) - sin (- 21 0^{\circ}) cot (33 0^{\circ})

11 sin (\frac{π}{2} + 0.1)

2^{2} - 4.9 (2) + 5.7 cos (0.01 (2))

cos (30 \circ)

1 - 3 \cdot cos (\frac{π}{2})