What is the value of 2/5 sin^2(60)+3cos^2(30)-tan^2(45) ?

The value of 2/5 sin^2(60)+3cos^2(30)-tan^2(45) is 31/20

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2/5 sin^2(60)+3cos^2(30)-tan^2(45)

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

\frac{31}{20}

Solution steps

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

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

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

= \frac{2}{5} (\frac{3}{2})^{2} + 3 (\frac{3}{2})^{2} - 1^{2}

Simplify

\frac{2}{5} (\frac{3}{2})^{2} + 3 (\frac{3}{2})^{2} - 1^{2} : \frac{31}{20}

= \frac{31}{20}

tan (\frac{11 π}{16})

tan (141 0^{\circ})

e^{1} - 2 cos (1)

cos^{2} (\frac{9 π}{8}) - cos (2 \cdot \frac{9 π}{8})

sin (- 132 0^{\circ})

What is the value of 2/5 sin^2(60)+3cos^2(30)-tan^2(45) ?
The value of 2/5 sin^2(60)+3cos^2(30)-tan^2(45) is 31/20