Prove 1 - 2 - x 2 - - x x - x - 2 x - - 1 - 2 2 - x x x x

1√(2)[x^2( x· x)+ x· 2x] =1√(2)(2x x x^2 x x) =1√(2)((2 x x)· x x) =RHS ...

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Byju's Answer

Standard XII

Mathematics

Domain and Range of Trigonometric Ratios

Prove 1 /√ 2...

Question

Prove
$\frac{1}{\sqrt{2}} [x^{2} \cdot (- csc x cot x) + csc x \cdot 2 x] = \frac{1}{\sqrt{2}} (2 - x cot x) x csc x$

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Solution

$\frac{1}{\sqrt{2}} [x^{2} (- csc x \cdot cot x) + csc x \cdot 2 x]$
$= \frac{1}{\sqrt{2}} (2 x csc x - x^{2} csc x cot x)$
$= \frac{1}{\sqrt{2}} ((2 - x cot x) \cdot x csc x)$ =RHS

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Prove1√2[x2⋅(−cscxcotx)+cscx⋅2x]=1√2(2−xcotx)xcscx

1√2[x2(−cscx⋅cotx)+cscx⋅2x]=1√2(2xcscx−x2cscxcotx)=1√2((2−xcotx)⋅xcscx)=RHS

Prove
$\frac{1}{\sqrt{2}} [x^{2} \cdot (- csc x cot x) + csc x \cdot 2 x] = \frac{1}{\sqrt{2}} (2 - x cot x) x csc x$

$\frac{1}{\sqrt{2}} [x^{2} (- csc x \cdot cot x) + csc x \cdot 2 x]$
$= \frac{1}{\sqrt{2}} (2 x csc x - x^{2} csc x cot x)$
$= \frac{1}{\sqrt{2}} ((2 - x cot x) \cdot x csc x)$ =RHS