In this discussion, we are going to verify trig identities using the sum and difference formulas.
Here is an outline of this discussion:
Verify that sin(x+pi/2) = cosx
Verify that tan(x-3pi/2) = -cotx
We begin with the left hand side of the equation and slowly manipulate it until it looks like the right hand side.
Verify that sin(x+pi/2) = cosx
LHS
= sin(x+pi/2)
= sinx * cospi/2 + cosx * sinpi/2
= sinx * 0 + cosx * 1
= 0 + cosx
= cosx
= RHS
Verify that tan(x-3pi/2) = -cotx
LHS
= tan(x-3pi/2)
= sin(x-3pi/2) / cos(x-3pi/2)
= [sinx * cos3pi/2 – cosx * sin3pi/2] / [cosx * cos3pi/2 + sinx * sin3pi/2]
= [sinx * 0 – cosx * -1] / [cosx * 0 + sinx * -1]
= cosx / -sinx
= -cotx
We have verified:
sin(x+pi/2) = cosx
tan(x-3pi/2) = -cotx.
Thank you for reading!
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➕MathAngel369➕
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