Answer:
The correct choice is B.
Step-by-step explanation:
a. Given
[tex]\cos^2(\theta)=\sin(\theta)\cos(\theta)[/tex]
We can subtract [tex]\sin(\theta)\cos(\theta)[/tex] from both sides to obtain;
[tex]\cos^2(\theta)-\sin(\theta)\cos(\theta)=0[/tex]
We can then factor [tex]\cos(\theta)[/tex] to obtain;
[tex]\cos(\theta)(\cos(\theta)-\sin(\theta))=0[/tex]
We can then proceed with our solution using the zero product principle.
b. Given [tex]\cos^2(\theta)=\sin(\theta)\cos(\theta)[/tex], it is not valid to divide both sides by [tex]\cos(\theta)[/tex] because [tex]\cos(\theta)[/tex] could be equal to zero and division by zero in disguise will not result in the true solutions of the given equation.
c. To solve sin2θ+2cosθsin2θ=0, first factor out the common factor of sin2θ on the left side.
This is also a justifiable approach.
d. To solve the equation sinθ+cosθ=1, first square both sides of the equation.
Squaring both sides will help solve the equation with double angle properties easily.
