What is expand sqrt((-asin(t)-asin(2t))^2+(acos(t)+acos(2t))^2) ?

The solution to expand sqrt((-asin(t)-asin(2t))^2+(acos(t)+acos(2t))^2) is sqrt(2)asqrt(1+cos(t))

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expand sqrt((-asin(t)-asin(2t))^2+(acos(t)+acos(2t))^2)

expand

(- a sin (t) - a sin (2 t))^{2} + (a cos (t) + a cos (2 t))^{2}

2 a 1 + cos (t)

Solution steps

(- a sin (t) - a sin (2 t))^{2} + (a cos (t) + a cos (2 t))^{2}

Expand

(- a sin (t) - a sin (2 t))^{2} + (a cos (t) + a cos (2 t))^{2} : a^{2} sin^{2} (t) + 2 a^{2} sin (t) sin (2 t) + a^{2} sin^{2} (2 t) + a^{2} cos^{2} (t) + 2 a^{2} cos (t) cos (2 t) + a^{2} cos^{2} (2 t)

= a^{2} sin^{2} (t) + 2 a^{2} sin (t) sin (2 t) + a^{2} sin^{2} (2 t) + a^{2} cos^{2} (t) + 2 a^{2} cos (t) cos (2 t) + a^{2} cos^{2} (2 t)

Factor

a^{2} sin^{2} (t) + 2 a^{2} sin (t) sin (2 t) + a^{2} sin^{2} (2 t) + a^{2} cos^{2} (t) + 2 a^{2} cos (t) cos (2 t) + a^{2} cos^{2} (2 t) : a^{2} \cdot 2 (1 + cos (t))

= a^{2} \cdot 2 (1 + cos (t))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 2 a^{2} cos (t) + 1

Apply radical rule:

assuming

a \geq 0

a^{2} = a

= 2 a cos (t) + 1

\frac{\partial}{\partial x} ((y) (3 x^{2} yz + 5 x z + 6))

f ((sin (x)) 2 x - 3)

164 (3 e^{4} + 4 e^{2} + 13)

(1 + e^{t}) (- e + e^{t})

\frac{x ^{2} + 1}{3 ( x - 8 )}

What is expand sqrt((-asin(t)-asin(2t))^2+(acos(t)+acos(2t))^2) ?
The solution to expand sqrt((-asin(t)-asin(2t))^2+(acos(t)+acos(2t))^2) is sqrt(2)asqrt(1+cos(t))