What is the value of 4cos^2(150)+3tan(225)+9csc^2(300) ?

The value of 4cos^2(150)+3tan(225)+9csc^2(300) is 18

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4cos^2(150)+3tan(225)+9csc^2(300)

4 cos^{2} (15 0^{\circ}) + 3 tan (22 5^{\circ}) + 9 csc^{2} (30 0^{\circ})

18

Solution steps

4 cos^{2} (15 0^{\circ}) + 3 tan (22 5^{\circ}) + 9 csc^{2} (30 0^{\circ})

tan (22 5^{\circ}) = tan (4 5^{\circ})

= 4 cos^{2} (15 0^{\circ}) + 3 tan (4 5^{\circ}) + 9 csc^{2} (30 0^{\circ})

Rewrite using trig identities:

csc^{2} (30 0^{\circ}) = 1 + cot^{2} (12 0^{\circ})

= 4 cos^{2} (15 0^{\circ}) + 3 tan (4 5^{\circ}) + 9 (1 + cot^{2} (12 0^{\circ}))

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

cot (12 0^{\circ}) = - \frac{3}{3}

= 4 (- \frac{3}{2})^{2} + 3 \cdot 1 + 9 1 + (- \frac{3}{3})^{2}

Simplify

4 (- \frac{3}{2})^{2} + 3 \cdot 1 + 9 1 + (- \frac{3}{3})^{2} : 18

= 18

2 cos (4 π)

cos (arcsin (\frac{7}{25}))

4 + 4 cos (\frac{π}{6})

20 cos (2)

arctan (\frac{- 3}{- 3})

What is the value of 4cos^2(150)+3tan(225)+9csc^2(300) ?
The value of 4cos^2(150)+3tan(225)+9csc^2(300) is 18