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 $\boxed{10\sin t + 26}$.

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 $\boxed{10\sin t + 26}$.