-1-sin3x sin x-dx-a- n -n - Z is equal to

The correct option is B 2(cosα+ x sinα)^1/2+C ∫dx√(sin^3xsin(x+α)) =∫dxsin^2x√(cosα + xsinα) = ∫ (cosα + xsinα)^ 12d( x) #160; = 2(co ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Common Angles

∫1√sin3x sin ...

Question

$\int \frac{1}{\sqrt{{sin}^{3} x sin (x + α)}} d x, a \neq n π, n ϵ Z$ is equal to

- 2 csc α (cos α - tan x sin α)^{1 / 2} + C

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- 2 (cos α + cot x sin α)^{1 / 2} + C

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- 2 csc α (cos α + cot x sin α)^{1 / 2} + C

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- 2 csc α (sin α + cot x cos α)^{1 / 2} + C

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Solution

The correct option is B $- 2 (cos α + cot x sin α)^{1 / 2} + C$
$\int \frac{d x}{\sqrt{{sin}^{3} x sin (x + α)}} = \int \frac{d x}{{sin}^{2} x \sqrt{cos α + cot x sin α}} = - \int (cos α + cot x sin α)^{- \frac{1}{2}} d (cot x)$
$= - 2 (cos α + cot x sin α)^{\frac{1}{2}} + C$

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Similar questions

\int \frac{1}{\sqrt{{sin}^{3} x sin (x + α)}} d x

$\int \frac{1}{\sqrt{s i n^{3} x s i n (x + α)}} d x .$

Q. If

{(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} . . . . . . . C_{n} x^{n}

, then

C_{0}^{2} + C_{1}^{2} + C_{2}^{2} + C_{3}^{2} + . . . . . . . + C_{n}^{2}

is equal to

" $\begin{matrix} T r i g o n o m e t r i c E q u a t i o n s & G e n e r a l S o l u t i o n s 1. s i n^{2} θ = s i n^{2} x & A . 2 n π \pm α 2. c o s^{2} θ = c o s^{2} x & B . n π + (- 1)^{n} α 3. t a n^{2} θ = t a n^{2} x & C . n π \pm α \end{matrix}$

Q. If

a + b + c = 0

then

\frac{1}{b^{2} + c^{2} - a^{2}} + \frac{1}{c^{2} + a^{2} - b^{2}} + \frac{1}{a^{2} + b^{2} - c^{2}}

is equal to

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∫1√sin3xsin(x+α)dx,a≠nπ,nϵZ is equal to

The correct option is B −2(cosα+cotxsinα)1/2+C∫dx√sin3xsin(x+α)=∫dxsin2x√cosα+cotxsinα=−∫(cosα+cotxsinα)−12d(cotx) =−2(cosα+cotxsinα)12+C

$\int \frac{1}{\sqrt{{sin}^{3} x sin (x + α)}} d x, a \neq n π, n ϵ Z$ is equal to

The correct option is B $- 2 (cos α + cot x sin α)^{1 / 2} + C$
$\int \frac{d x}{\sqrt{{sin}^{3} x sin (x + α)}} = \int \frac{d x}{{sin}^{2} x \sqrt{cos α + cot x sin α}} = - \int (cos α + cot x sin α)^{- \frac{1}{2}} d (cot x)$
$= - 2 (cos α + cot x sin α)^{\frac{1}{2}} + C$