Question

Use trig identities to verify this expression:
((1-tan^2(x))/(sec^2(x))=cos(2x).

Answer 1

Answer:

See below

Step-by-step explanation:

Verify the expression:

((1-tan^2(x))/(sec^2(x))=cos(2x)

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• (1-tan^2(x))/(sec^2(x) =
• (1-tan^2(x))/(1/cos^2(x) =
• (1-tan^2(x))*cos^2(x) =
• cos^2(x) - sin^2(x) =
• cos^2(x) - (1 - cos^2(x)) =
• 2cos^2(x) - 1 =
• cos(2x)

Done