5sin п/4 + 3tg п/4 - 5cos п/4-10 ctg п/4

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To simplify this expression, we can convert all trigonometric functions to the same base, which in this case will be sine and cosine.

Given
5sin (π/4) + 3tan (π/4) - 5cos (π/4) - 10cot (π/4)

We know that tan (π/4) = sin (π/4) / cos (π/4) = 1, and cot (π/4) = cos (π/4) / sin (π/4) = 1.

So, the expression becomes
5sin(π/4) + 3(1) - 5cos(π/4) - 10(1
= 5(√2/2) + 3 - 5(√2/2) - 10

Simplifying further
= 5√2/2 + 3 - 5√2/2 - 1
= 8 - 1
= -2

Therefore, the simplified expression is -2.