化简 (sqrt((-asin(t))^2+(bcos(t))^2))^3

解答

化简

((- a sin (t))^{2} + (b cos (t))^{2})^{3}

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

求解步骤

((- a sin (t))^{2} + (b cos (t))^{2})^{3}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

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

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

使用指数法则:

(n a)^{n} = a,

假定

n i s o dd or a \geq 0

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

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

(- a sin (t))^{2} = a^{2} sin^{2} (t)

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

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

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

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

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