What is sin(t)(cos(2t))^2(cos(3t))^2 ?

The solution to sin(t)(cos(2t))^2(cos(3t))^2 is cos^2(2t)cos^2(3t)sin(t)

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simplify sin(t)(cos(2t))^2(cos(3t))^2

simplify

sin (t) (cos (2 t))^{2} (cos (3 t))^{2}

cos^{2} (2 t) cos^{2} (3 t) sin (t)

Solution steps

sin (t) (cos (2 t))^{2} (cos (3 t))^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

(cos (2 t))^{2} (cos (3 t))^{2} = (cos (2 t) cos (3 t))^{2}

= sin (t) (cos (2 t) cos (3 t))^{2}

(cos (2 t) cos (3 t))^{2} = cos^{2} (2 t) cos^{2} (3 t)

= cos^{2} (2 t) cos^{2} (3 t) sin (t)

e^{- \frac{17}{3}} \cdot (- 24)

- 1

6.282 \cdot 1 0^{- 5}

(2.192 \cdot 1 0^{- 7}) x^{5}

What is sin(t)(cos(2t))^2(cos(3t))^2 ?
The solution to sin(t)(cos(2t))^2(cos(3t))^2 is cos^2(2t)cos^2(3t)sin(t)