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otez555 [7]
3 years ago
3

Prove : 1+cosA-sin2A/sinA*(1+cosA)= cotA

Mathematics
1 answer:
ladessa [460]3 years ago
5 0
\dfrac{1+\cos A-\sin^2A}{\sin A(1+\cos A)}=\cot A\\\\L_s=\dfrac{(1-\sin^2A)+\cos A}{\sin A(1+\cos A)}=\dfrac{\cos^2A+\cos A}{\sin A(1+\cos A)}\\\\=\dfrac{\cos A(1+\cos A)}{\sin A(1+\cos A)}=\dfrac{\cos A}{\sin A}=\cot A=R_s\\\\\text{Used:}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\\cot x=\dfrac{\cos x}{\sin x}
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Step-by-step explanation:

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Solve the equation:<br><br> a) -3 = 7+2t/3<br><br> b) 4(5x-2) = 7(2x+3) <br><br> c) 2x-6 = 30-2.5x
Umnica [9.8K]
Let's start by solving the first equation.

a) -3 = 7 + 2t/3 
To begin simplifying this equation, we should multiply both sides by 3 to get rid of the denominator on the right side of the equation.
-9 = 7 + 2t
Next, we should subtract 7 from both sides to cancel out the 7 on the right side.
-16 = 2t
Finally, we should divide both sides by 2.
t= -8


Now let's move on to the next equation.

b) 4(5x-2) = 7(2x+3)
Let's use the distributive property to get rid of the parentheses and their coefficients.
20x-8 = 14x + 21

Now, lets subtract 14x from both sides of the equation.

6x - 8 = 21

Next, let's add 8 to both sides of the equation.

6x = 29

And divide both sides by the coefficient of x, which is 6.

x = 29/6 or 4 5/6

Now for the last equation.

C) 2x - 6 = 20 - 2.5x
First, we should add 2.5x to both sides to cancel out the -2.5x on the right side of the equation.
4.5x - 6 = 20
Now, let's add 6 to both sides to get the variable term alone.
4.5x = 26
Finally, we should divide both sides by 4.5 to get x by itself.
x = 5 7/9

Hope this helps! :)
7 0
4 years ago
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