Question 1

[![](http://latex.codecogs.com/gif.latex?1&space;&plus;&space;tan%5E%7B2%7D%5CTheta 1 + tan^{2}\Theta)](http://www.codecogs.com/eqnedit.php?latex=1&space;&plus;&space;tan%5E%7B2%7D%5CTheta)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?sec%5E%7B2%7D%5CTheta sec^{2}\Theta)](http://www.codecogs.com/eqnedit.php?latex=sec%5E%7B2%7D%5CTheta)

Question 2

[![](http://latex.codecogs.com/gif.latex?1&space;&plus;&space;cot%5E%7B2%7D%5CTheta 1 + cot^{2}\Theta)](http://www.codecogs.com/eqnedit.php?latex=1&space;&plus;&space;cot%5E%7B2%7D%5CTheta)

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?csc%5E%7B2%7D%5CTheta csc^{2}\Theta)](http://www.codecogs.com/eqnedit.php?latex=csc%5E%7B2%7D%5CTheta)

Question 3

sin2x

Accepted Answer

2 sinx cosx

Question 4

cos2x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?cos%5E%7B2%7Dx&space;-&space;sin%5E%7B2%7Dx cos^{2}x - sin^{2}x)](http://www.codecogs.com/eqnedit.php?latex=cos%5E%7B2%7Dx&space;-&space;sin%5E%7B2%7Dx)

Question 5

tan2x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B2%5C&space;tanx%7D%7B1-tan%5E%7B2%7Dx%7D \frac{2\ tanx}{1-tan^{2}x})](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B2%5C&space;tanx%7D%7B1-tan%5E%7B2%7Dx%7D)

Question 6

sin'x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;sinx&space;=&space;cosx \frac{\mathrm{d} }{\mathrm{d} x}\ sinx = cosx)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;sinx&space;=&space;cosx)

Question 7

cos'x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;cosx&space;=&space;-sinx \frac{\mathrm{d} }{\mathrm{d} x}\ cosx = -sinx)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;cosx&space;=&space;-sinx)

Question 8

tan'x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;tanx&space;=&space;sec%5E%7B2%7Dx \frac{\mathrm{d} }{\mathrm{d} x}\ tanx = sec^{2}x)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;tanx&space;=&space;sec%5E%7B2%7Dx)

Question 9

csc'x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;cscx&space;=&space;1-&space;cscx%5C&space;cotx \frac{\mathrm{d} }{\mathrm{d} x}\ cscx = 1- cscx\ cotx)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;cscx&space;=&space;1-&space;cscx%5C&space;cotx)

Question 10

sec'x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;secx&space;=&space;secx%5C&space;tanx \frac{\mathrm{d} }{\mathrm{d} x}\ secx = secx\ tanx)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;secx&space;=&space;secx%5C&space;tanx)

Question 11

cot'x

Accepted Answer

[![](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;cotx&space;=&space;-csc%5E%7B2%7Dx \frac{\mathrm{d} }{\mathrm{d} x}\ cotx = -csc^{2}x)](http://www.codecogs.com/eqnedit.php?latex=%5Cfrac%7B%5Cmathrm%7Bd%7D&space;%7D%7B%5Cmathrm%7Bd%7D&space;x%7D%5C&space;cotx&space;=&space;-csc%5E%7B2%7Dx)

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