Answer:
Proved that [tex] 1 - 2\sin ^{2}x = 2\cos ^{2} x - 1[/tex].
Step-by-step explanation:
We know the following identity as [tex]\sin ^{2} x + \cos ^{2} x =1[/tex] .......... (1) and we commonly use this identity as a formula.
Now, rearranging the identity we get
[tex]\sin ^{2}x = 1 - \cos ^{2} x[/tex]
⇒ [tex]2\sin ^{2}x = 2 - 2\cos ^{2} x[/tex]
⇒ [tex] - 2\sin ^{2}x = 2\cos ^{2} x - 2[/tex]
⇒ [tex] 1 - 2\sin ^{2}x = 1 + 2\cos ^{2} x - 2[/tex]
⇒[tex] 1 - 2\sin ^{2}x = 2\cos ^{2} x - 1[/tex]
Hence, proved that [tex] 1 - 2\sin ^{2}x = 2\cos ^{2} x - 1[/tex]. (Answer)
