What is 3sin^2(a)-6-3cos^2(a) ?

The solution to 3sin^2(a)-6-3cos^2(a) is -3cos(2a)-6

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simplify 3sin^2(a)-6-3cos^2(a)

simplify

3 sin^{2} (a) - 6 - 3 cos^{2} (a)

- 3 cos (2 a) - 6

Solution steps

3 sin^{2} (a) - 6 - 3 cos^{2} (a)

Use the Double Angle identity:

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

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

= 3 (- 2 - cos (2 a))

Factor

3 sin^{2} (a) - 6 - 3 cos^{2} (a) : 3 (sin^{2} (a) - 2 - cos^{2} (a))

= 3 (- cos (2 a) - 2)

Expand

3 (- cos (2 a) - 2) : - 3 cos (2 a) - 6

= - 3 cos (2 a) - 6

x^{2} + 2 3 x + 3

\frac{1}{2} an - 1 + 1

(3 x^{2} y + 4 x y^{2})^{3}

\frac{( ( - k ) ^{3} \cdot x - k ^{4} )}{( k ^{- 3} \cdot x ( - k ^{6} ) )}

a^{3} b + b^{3}

What is 3sin^2(a)-6-3cos^2(a) ?
The solution to 3sin^2(a)-6-3cos^2(a) is -3cos(2a)-6