What is the value of 2(cos^2(15)-sin^2(15)) ?

The value of 2(cos^2(15)-sin^2(15)) is square root of 3

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2(cos^2(15)-sin^2(15))

2 (cos^{2} (1 5^{\circ}) - sin^{2} (1 5^{\circ}))

3

Decimal Notation

1.73205 \dots

Solution steps

2 (cos^{2} (1 5^{\circ}) - sin^{2} (1 5^{\circ}))

Rewrite using trig identities:

cos^{2} (1 5^{\circ}) - sin^{2} (1 5^{\circ}) = cos (3 0^{\circ})

cos^{2} (1 5^{\circ}) - sin^{2} (1 5^{\circ})

Use the Double Angle identity:

cos^{2} (x) - sin^{2} (x) = cos (2 x)

= cos (2 \cdot 1 5^{\circ})

Simplify

= cos (3 0^{\circ})

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

Use the following trivial identity:

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

cos (3 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 2 \cdot \frac{3}{2}

Simplify

2 \cdot \frac{3}{2} : 3

2 \cdot \frac{3}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 2}{2}

Cancel the common factor:

2

= 3

= 3

- 4 sin (\frac{3 π}{4})

tan (- \frac{13 π}{12})

cosh (9)

tanh (2)

sin^{4} (0)

What is the value of 2(cos^2(15)-sin^2(15)) ?
The value of 2(cos^2(15)-sin^2(15)) is square root of 3