Problem

16. An equivalent expression to sin⁡x+cos⁡xcsc⁡x+sec⁡x is

Answer

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Answer

sin⁡(2x)2

Steps

Step 1 ：An equivalent expression to sin⁡x+cos⁡xcsc⁡x+sec⁡x is

Step 2 ：Convert the expression into sine and cosine terms: sin⁡x+cos⁡x1sin⁡x+1cos⁡x

Step 3 ：Find a common denominator for the denominator: sin⁡x+cos⁡xsin⁡x+cos⁡xsin⁡xcos⁡x

Step 4 ：Simplify the expression: sin⁡xcos⁡x(sin⁡x+cos⁡x)sin⁡x+cos⁡x

Step 5 ：Cancel out the common terms: sin⁡xcos⁡x

Step 6 ：Use the double angle identity: sin⁡(2x)2

Step 7 ：sin⁡(2x)2

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