Question

Please help me with this question

Answer 1

`cos(x-(3\pi )/(2) )= (-3)/(4) cos(x)`

Explanation:

Lets remember the following expression:

cos(x-a)= cos(x)*cos(a)+sin(x)*sin(a)

if a= -3 pi /2 then:

cos(x-3 pi/2)= cos(x)*cos(3pi/2) + sin(x)*sin(3pi/2)

Since cos (3pi/2) is located exactly at 'y' axis, its value=0

Moreover sin(3pi/2)= -1 because, that angle is located at 'y' axis, negative side

cos(x-3pi/2)= -sin(x)

But, we can simplify a little more since we now that tan(x)=3/4

That means that sin(x)/cos(x)= 3/4, from that expression we isolate sin(x) and we obtain that sin(x)=cos(x) * 3/4

Using the above conclusion we have that

cos(x-3pi/2)= -cos(x)*3/4