# Maths Help!!! (1 Viewer)

#### atar90plus

##### 01000101=YES! YES! YES!
Hello

Simplify

Q2. c) sec x cot x
i) 5cot^2 x + 5
l) cot x -cotx cos^2 x

Prove that

Q3. a) cos^2 x-1 = -sin^2x
c) 3+3tan^2 x = 3 / 1-sin^2 x
d) sec^2 x -tan^2 x = cosec^2x -cot^2x
g) cos^2 (90-x)cotx = sinx cosx

#### deswa1

##### Well-Known Member
For 2c)
(secx)(cotx)=(1/cosx)(cosx/sinx)=1/sinx

For 2i) 5(cot^2x+1)=5(cosec^2x) (on using cot^2x+1=cosec^2x)

For 2l) cotx(1-cos^2x)=cotx(sinx)=(cosx/sinx)(sinx)=cosx

Sorry about the lack of latex- I don't have much time now

#### EpikHigh

##### Arizona Tears
$\bg_white Q3 A)\\\\Cos^2x - 1 = -Sin^2x \\\\ Cos^2x - 1 = LHS \\\\ Sin^2x + Cos^2x = 1 \\\\ Sin^2x + Cos^2x - 1 = 0 \\\\ Cos^2x - 1 = -Sin^2x \\\\ LHS = RHS$

Last edited:

#### theind1996

##### Active Member
For 2c)
(secx)(cotx)=(1/cosx)(cosx/sinx)=1/sinx

For 2i) 5(cot^2x+1)=5(cosec^2x) (on using cot^2x+1=cosec^2x)

For 2l) cotx(1-cos^2x)=cotx(sinx)=(cosx/sinx)(sinx)=cosx

Sorry about the lack of latex- I don't have much time now
Lol that could be interpreted so differently.

#### qwerty44

##### Member
\bg_white \begin{align*}&3(c)\\&LHS=3+\frac{3sin^{2}x}{cos^{2}x}\\\\&=\frac{3cos^{2}x+3sin^{2}x}{cos^{2}x}\\\\&=\frac{3(sin^2{x}+cos^2{x})}{1-sin^2{x}}\\\\&=\frac{3}{1-sin^2{x}}\\\\&=RHS\end{align*}

#### EpikHigh

##### Arizona Tears
\bg_white \begin{align*}&3(c)\\&LHS=3+\frac{3sin^{2}x}{cos^{2}x}\\\\&=\frac{3cos^{2}x+3sin^{2}x}{cos^{2}x}\\\\&=\frac{3(sin^2{x}+cos^2{x})}{1-sin^2{x}}\\\\&=\frac{3}{1-sin^2{x}}\\\\&=RHS\end{align*}
Nicely done I just did that question haha, I need to learn how to use LaTeX :L

#### deswa1

##### Well-Known Member
For d, both LHS and RHS are equal to one (using cosec^2-cot^2 and sec^2-tan^2).

For g) cos^2(90-x)cotx=sin^2xcotx=(sinx)(sinx)(cosx)/(sinx)=(sinx)(cosx) -> The trick with this one is cos(90-x)=sinx

#### Carrotsticks

##### Retired
Moved to Mathematics.

#### qwerty44

##### Member
$\bg_white 3(d)\\\\&LHS=\frac{1}{cos^2{x}}+\frac{sin^{2}x}{cos^{2}x}\\\\&=\frac{1-sin^{2}x}{cos^{2}x}\\\\&=\frac{cos^2{x}}{cos^2{x}}\\\\&=1\\\\&RHS=\frac{1}{sin^2{x}}+\frac{cos^{2}x}{sin^{2}x}\\\\&=\frac{1-cos^{2}x}{sin^{2}x}\\\\&=\frac{sin^2{x}}{sin^2{x}}\\\\&=1\\\\&=LHS$

EDIT: Beaten again D:

#### gr_111

##### Member
Nicely done I just did that question haha, I need to learn how to use LaTeX :L
Have a look at http://www.codecogs.com/latex/eqneditor.php. You can start by using the buttons to work out what does what, and you can either save formula as a pic and attach or copy the code from the bottom and paste into these forums.