What is tan^2(a)(2*cos^2(a)+sin^2(a)-1) ?

The solution to tan^2(a)(2*cos^2(a)+sin^2(a)-1) is sin^2(a)

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simplify tan^2(a)(2*cos^2(a)+sin^2(a)-1)

simplify

tan^{2} (a) (2 \cdot cos^{2} (a) + sin^{2} (a) - 1)

sin^{2} (a)

Solution steps

tan^{2} (a) (2 cos^{2} (a) + sin^{2} (a) - 1)

Use the Pythagorean identity:

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

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

= tan^{2} (a) (2 cos^{2} (a) - cos^{2} (a))

cos^{2} (a) tan^{2} (a) = sin^{2} (a)

= sin^{2} (a)

Factor

2 cos^{2} (a) - cos^{2} (a) : cos^{2} (a)

= sin^{2} (a)

(9 - x^{2})^{2} d x

\frac{( x ^{2} + 1 ) ^{4}}{( 2 x + 1 ) ^{3} ( 3 x - 1 ) ^{5}}

(x^{2} - \frac{1}{2 x})^{3}

\frac{3 ( - x ^{2} - 1 )}{( x ^{2} - 1 ) ^{2}}

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

What is tan^2(a)(2*cos^2(a)+sin^2(a)-1) ?
The solution to tan^2(a)(2*cos^2(a)+sin^2(a)-1) is sin^2(a)