Show that 2cos^2theta - 1 = cos^2theta - sin^2theta
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Answer:
Step-by-step explanation:Given: Prove
sin
2
θ
−
cos
2
θ
=
1
−
2
cos
2
θ
Use the Pythagorean Identity:
sin
2
θ
+
cos
2
θ
=
1
Rearrange the identity:
sin
2
θ
=
1
−
cos
2
θ
Start with the left side of the equation and substitute the rearranged identity:
sin
2
θ
−
cos
2
θ
=
1
−
cos
2
θ
−
cos
2
θ
Combine like-terms:
=
1
−
2
cos
2
θ
This is the right-side
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