What is expand sin^2(u)(v^2+1)+cos^2(u)(v^2+1)+v^2 ?

The solution to expand sin^2(u)(v^2+1)+cos^2(u)(v^2+1)+v^2 is v^2+v^2cos^2(u)+v^2sin^2(u)+1

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expand sin^2(u)(v^2+1)+cos^2(u)(v^2+1)+v^2

expand

sin^{2} (u) (v^{2} + 1) + cos^{2} (u) (v^{2} + 1) + v^{2}

v^{2} + v^{2} cos^{2} (u) + v^{2} sin^{2} (u) + 1

Solution steps

sin^{2} (u) (v^{2} + 1) + cos^{2} (u) (v^{2} + 1) + v^{2}

Expand

sin^{2} (u) (v^{2} + 1) : sin^{2} (u) v^{2} + sin^{2} (u)

= sin^{2} (u) v^{2} + sin^{2} (u) + cos^{2} (u) (v^{2} + 1) + v^{2}

Expand

cos^{2} (u) (v^{2} + 1) : cos^{2} (u) v^{2} + cos^{2} (u)

= sin^{2} (u) v^{2} + sin^{2} (u) + cos^{2} (u) v^{2} + cos^{2} (u) + v^{2}

Use the Pythagorean identity:

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

= v^{2} + v^{2} cos^{2} (u) + v^{2} sin^{2} (u) + 1

(\times + \frac{1}{2}) (x - \frac{1}{2})

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

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

((a + b F + c F^{2})^{2}) F^{2} \cdot (1 - d F - e F^{2})

(tan (θ) + 1) (cos (θ) - 1)

What is expand sin^2(u)(v^2+1)+cos^2(u)(v^2+1)+v^2 ?
The solution to expand sin^2(u)(v^2+1)+cos^2(u)(v^2+1)+v^2 is v^2+v^2cos^2(u)+v^2sin^2(u)+1