Find a “nice" (i.e. algebraic) expression for tan(sec-1(t)) for negative t-values.

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A: Range of trigonometric function

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Q: 5. Simplify the expression: tan (csc (x)). Assume x is defined appropriately.

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Q: snip

A: Given that - f(θ) = tanθ = 3            ..........(1)Substituting π+θ in equation (1) - fπ+θ =…

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A: Introduction :

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A: To find the value of ddxtanxx=π3.

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A: To find:

Q: find the derivative. y = (tan −1 x)3

A: Use power rule and chain rule.

Q: tan (0 + 120) = 0

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Q: Given that tan(x)=−3.4, what is tan(−x)?

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Q: If y = tan-1(-1), find the value of y without use Calculator.

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A: Given: y=2x3-tan(x) Quotient rule for derivative fg'=f'.g-g'fg2

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.