Question

Solve cos x tan x - sin2x = 0 for all real values of x.

Solve 2 sin2x – sin x = 0 for principal values of x.

Write the equation 3x + 4y – 7 = 0 in normal form.

Write the standard form of the equation of a line for which the length of the normal is 3 and the normal makes an angle of 135° with the positive x–axis.

Answer 1

if you can explain each one and how to do them i would be grateful! :)

Answer 2

HINT: \[\tan(x) = \frac{ \sin(x) }{ \cos(x) }\] \[\sin(2x)= 2\sin(x)\cos(x)\]

Answer 3

im still lost .. lol

Answer 4

\[x \left( \frac{ \sin(x) }{ \cos(x) } \right) -2\sin(x)\cos(x) = \frac{ xsin(x) }{ \cos(x) }-2\sin(x)\cos(x)=0\]
put everything into one single fraction and solve.

For the second one: \[2(2\sin(x)\cos(x))-\sin(x)=4(\sin(x)\cos(x)-\sin(x) = 0\]
factor out sin(x) and find the values when sin(x)=0 and when 4cos(x)-1 = 0

Answer 5

okay, thank you !