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Satyam C.
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Trigonometry
TutorMe
Question:

If cos(x+y)=$$ \frac{4}{5} $$ and sin(x-y)=$$ \frac{5}{13} $$ Find tan(2x)??

Satyam C.
Answer:

=tan(2x) =tan(x+y+x-y) =$$ \frac{tan(x+y)+tan(x-y)}{1-tan(x+y)tan(x-y)} $$ =$$ \frac{ \frac{3}{4}*\frac{5}{12} }{1-\frac{3}{4}*\frac{5}{12}} $$ =$$\frac{5}{11}$$

Calculus
TutorMe
Question:

$$ \int xsinx,\mathrm{d}x $$

Satyam C.
Answer:

x$$ \frac{-cos2x}{2} $$ - $$ \int \frac{-cos2x}{2},\mathrm{d}x $$ $$ \frac{-xcos2x}{2} $$ +$$ \frac{1}{2} $$$$ \int \frac{cos2x}{2},\mathrm{d}x $$ $$ \frac{-xcos2x}{2} $$+$$ \frac{1}{2} $$$$ \frac{sin2x}{2} $$+k $$ \frac{-xcos2x}{2} $$+$$ \frac{sin2x}{4} $$+k

Algebra
TutorMe
Question:

solve for x: |x-2|=|2x-6|

Satyam C.
Answer:

a point at which nature change are x=2, 3 case 1: For x<2 -(x-2)=-(2x-6) x-2=2x-6 x=4 But we have assume x<2, this is not possible case 2: For 2<x<3 x-2=-(2x-6) x-2=6-2x 3x=8 x=8/3 case 3: For x>3 x-2=2x-6 x=4 Hence, solution is x=8/3 and x=4

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