Perform the indicated operation and simplify the result so that there are no quotients.
$(5 + \sin t)^{2} + \cos^{2} t$
The simplified form, with no quotients, of $(5 + \sin t)^{2} + \cos^{2} t$ is (Do not factor.)

Answer

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Answer

The simplified form, with no quotients, of $(5 + \sin t)^{2} + \cos^{2} t$ is $10 \sin t + 26$ .

Steps

Step 1 ：Given the expression $(5 + \sin t)^{2} + \cos^{2} t$ .

Step 2 ：Expand the square to get $\sin (t)^{2} + 10 \sin (t) + \cos (t)^{2} + 25$ .

Step 3 ：Use the Pythagorean identity $\sin^{2} t + \cos^{2} t = 1$ to simplify the expression further.

Step 4 ：The simplified form, with no quotients, of $(5 + \sin t)^{2} + \cos^{2} t$ is $10 \sin t + 26$ .