What is the value of cos^2(30)-sin^2(135)+8sin(45)cos(135) ?

The value of cos^2(30)-sin^2(135)+8sin(45)cos(135) is -15/4

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cos^2(30)-sin^2(135)+8sin(45)cos(135)

cos^{2} (3 0^{\circ}) - sin^{2} (13 5^{\circ}) + 8 sin (4 5^{\circ}) cos (13 5^{\circ})

- \frac{15}{4}

Solution steps

cos^{2} (3 0^{\circ}) - sin^{2} (13 5^{\circ}) + 8 sin (4 5^{\circ}) cos (13 5^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

= (\frac{3}{2})^{2} - (\frac{2}{2})^{2} + 8 \cdot \frac{2}{2} (- \frac{2}{2})

Simplify

(\frac{3}{2})^{2} - (\frac{2}{2})^{2} + 8 \cdot \frac{2}{2} (- \frac{2}{2}) : - \frac{15}{4}

= - \frac{15}{4}

18 cos (4 5^{\circ})

cos (\frac{3 \cdot π}{2})

5 cos (\frac{5 π}{4})

cos (\frac{3 \cdot π}{4})

sec^{2} (1 2^{\circ})

What is the value of cos^2(30)-sin^2(135)+8sin(45)cos(135) ?
The value of cos^2(30)-sin^2(135)+8sin(45)cos(135) is -15/4