Answer:
option B is correct.
[tex]2\sin^2r - 1[/tex]
Step-by-step explanation:
Given the expression: [tex]1-2\cos^2r[/tex] ......[1]
Using trigonometric identities:
[tex]\sin^2r+ \cos^2r = 1[/tex]
We can rearrange this as;
[tex]\cos^2r = 1-\sin^2r[/tex] ......[2]
Substitute equation [2] into [1] we get;
[tex]1-2(1-\sin^2r)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a \cdot b + a\cdot c[/tex]
[tex]1- 2 +2sin^2r[/tex]
or
[tex]-1+2\sin^2r[/tex]
therefore, the given expression in terms of sine terms is; [tex]2\sin^2r-1[/tex]
