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ELEN [110]
3 years ago
14

Show all steps necessary to verify the trigonometric identity: 1 - 2cos2 x = 2sin2 x - 1

Mathematics
1 answer:
padilas [110]3 years ago
6 0

ANSWER

See explanation.

EXPLANATION

We want to very the identity:

1 - 2 \cos^{2} (x) = 2 \sin^{2} (x) - 1

Let us take the Left hand side and work it out to get the right hand side.

1 - 2 \cos^{2} (x)

Recall the Pythagorean Identity:

\cos^{2} (x) +  \sin^{2} (x) = 1

Make cos²(x) the subject.

\cos^{2} (x) = 1 -  \sin^{2} (x)

We substitute this into our expression to get:

1 - 2 (1 -  \sin^{2} (x) )

Expand:

1 - 2 + 2\sin^{2} (x)

Simplify

- 1+ 2\sin^{2} (x)

We can rewrite to get;

2\sin^{2} (x)  - 1

Therefore:

1 - 2 \cos^{2} (x) = 2 \sin^{2} (x) - 1

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