Using Trigonometric Identities In Exercises 81 and 82, use trigonometric identities to transform one side of the equation into the other. cot⁡θ+tan⁡θcot⁡θ=sec2θ

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Using Trigonometric Identities In Exercises 81 and 82, use trigonometric identities to transform one side of the equation into the other.  cot⁡θ+tan⁡θcot⁡θ=sec2θ

hajavaF · Accepted Answer

To determine  To Transform: one side of the equation into the other  Explanation of Solution  Given information: cot⁡θ+tan⁡θcot⁡θ=sec2θ  Concept used:  Quotient Identities:  tan⁡θ=sin⁡θcos⁡θ  cot⁡θ=cos⁡θsin⁡θ  Pythagorean Identities:  1+tan2θ=sec2θ  Calculation:  Work on the left side’s expression to convert it to sec2θ. Start by dividing  cos⁡θ+tan⁡θcot⁡θ=1+tan⁡θcot⁡θ  cos⁡θ+tan⁡θcot⁡θ=1+sin⁡θcos⁡θcos⁡θsin⁡θ  cos⁡θ+tan⁡θcot⁡θ=1+sin2θcos2θ  cos⁡θ+tan⁡θcot⁡θ=1+tan2θ  Use Pythagorean Identities  1+tan2θ=sec2θ  cot⁡θ+tan⁡θcot⁡θ=sec2θ

Using Trigonometric Identities In Exercises 81 and 82, use trigonometric identit

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