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Simplify to a single trig function with no denominator. 5sec^(2)x-5tan^(2)x

Simplify to a single trig function with no denominator.\newline5sec⁡2x−5tan⁡2x5\sec^{2}x-5\tan^{2}x

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Full solution

Q. Simplify to a single trig function with no denominator.\newline5sec⁡2x−5tan⁡2x5\sec^{2}x-5\tan^{2}x
  1. Recognize identity: Recognize a trigonometric identity:\newlineUsing the identity sec⁡2(x)−tan⁡2(x)=1\sec^2(x) - \tan^2(x) = 1, we can factor out the common term 55 from the original expression.\newlineCalculation: 5(sec⁡2(x)−tan⁡2(x))5(\sec^2(x) - \tan^2(x))
  2. Apply identity: Apply the identity:\newlineSubstitute the identity into the expression.\newlineCalculation: 5(1)=55(1) = 5

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