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

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})

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

Use the following trivial identity:

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

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

Simplify

2 \cdot \frac{3}{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