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Find the value of t which satisfies (t-[...

Find the value of t which satisfies (t-[|sinx|]!=3!5! Where [.] denotes the greatest integer function.

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To solve the equation \( t - [|\sin x|] = 3! \times 5! \), where \([.]\) denotes the greatest integer function, we will follow these steps: ### Step 1: Understand the range of \(|\sin x|\) The value of \(|\sin x|\) lies between 0 and 1. Therefore, the greatest integer function \([|\sin x|]\) can take two possible values: - \([|\sin x|] = 0\) when \(|\sin x| < 1\) - \([|\sin x|] = 1\) when \(|\sin x| = 1\) ### Step 2: Calculate \(3! \times 5!\) ...
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