Do you want a general solution or from 0 <= x < 2pi?
tan^2(2x) - 1 = 0
tan^2(2x) = 1
Take the square root of both sides,
tan(2x) = +/- 1
Two equations:
tan(2x) = 1
tan(2x) = -1
Solve each equation.
tan(2x) = 1, 2x = {pi/4, 5pi/4, 9pi/4, 13pi/4},
x = { pi/8, 5pi/8, 9pi/8, 13pi/8 }
tan(2x) = -1, 2x = { 3pi/4, 7pi/4, 11pi/4, 15pi/4 },
x = { 3pi/8, 7pi/8, 11pi/8, 15pi/8}
So for solutions within [0, 2pi),
x = {pi/8, 3pi/8, 5pi/8, 7pi/8, 9pi/8, 11pi/8, 13pi/8, 15pi/8 }
<h2><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u><u>-</u></h2>
Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3 ?
<h2><u>Solution</u>:-</h2>
Let the given points be A(-1,7) and B(4,-3)
Now,
Let the point be P(x, y) which divides AB in the ratio 2:3
Here,
<h3>

</h3>
Where,
= 2 ,
= 3
= -1 ,
= 4
Putting values we get,
x = 
x = 
x = 
x = 1
Now,
Finding y
<h3>

</h3>
Where,
= 2 ,
= 3
= 7 ,
= -3
Putting values we get,
y = 
y = 
y = 
y = 3
Hence x = 1, y = 3
So, the required point is P(x, y)
= P(1, 3)
<h3>The coordinates of the point is P(1, 3). [Answer]</h3>
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<u>N</u><u>o</u><u>t</u><u>e</u>:- Refer the attachment.
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-2c - 8 = -10c
+2c +2c
-8 = -8c
divide by -8
1 = c
2c + 8= 10c
-2c -2c
8 = 8c
divide by 8
1 =c
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