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Exercise

(1+tan⁡2(x))cos⁡(x)+sec⁡(x)\left(1+\tan^2\left(x\right)\right)\cos\left(x\right)+\sec\left(x\right)

Step-by-step Solution

1

Applying the trigonometric identity: 1+tan⁡(θ)2=sec⁡(θ)21+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2

sec⁡(x)2cos⁡(x)+sec⁡(x)\sec\left(x\right)^2\cos\left(x\right)+\sec\left(x\right)
Why is tan(x)^2+1 = sec(x)^2 ?

Final answer to the exercise

sec⁡(x)2cos⁡(x)+sec⁡(x)\sec\left(x\right)^2\cos\left(x\right)+\sec\left(x\right)

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(1+tan2(x))cos(x)+sec(x)
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