.d/dx[cos(x)] =d/dx [ 1/sin(x) ] = d/dx[sin(x)]/sin^2(x) = cos(x)/sin^2(x) Rewrite/simplify: = cot(x)cosec(x) | =d/dx [ 1/sin(x) ] = d/dx[sin(x)]/sin^2(x) ...

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Byju's Answer

Standard XII

Mathematics

Integration of Irrational Algebraic Fractions - 2

y=cosecx=1/si...

Question

y=cosec $\frac{x = 1}{s i n x}$

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Solution

$\begin{matrix} \frac{d}{d x} [c o s (x)] = \frac{d}{d x} [\frac{1}{s i n (x)}] = - \frac{\frac{d}{d x} [s i n (x)]}{s i n^{2} (x)} = - \frac{c o s (x)}{s i n^{2} (x)} R e w r i t e / s i m p l i f y : = - c o t (x) c o s e c (x) \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} = \frac{d}{d x} [\frac{1}{s i n (x)}] = - \frac{\frac{d}{d x} [s i n (x)]}{s i n^{2} (x)} = - \frac{c o s (x)}{s i n^{2} (x)} R e w r i t e / s i m p l i f y : = - c o t (x) c o s e c (x) \end{matrix}$

Suggest Corrections

y=cosec x=1sinx

ddx[cos(x)]=ddx[1sin(x)]=−ddx[sin(x)]sin2(x)=−cos(x)sin2(x)Rewrite/simplify:=−cot(x)cosec(x)∣∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣∣=ddx[1sin(x)]=−ddx[sin(x)]sin2(x)=−cos(x)sin2(x)Rewrite/simplify:=−cot(x)cosec(x)

y=cosec $\frac{x = 1}{s i n x}$