What is the limit as x approaches pi/2 of (5(sin(x)-1))/(cos^2(x)) ?

The limit as x approaches pi/2 of (5(sin(x)-1))/(cos^2(x)) is -5/2

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limit as x approaches pi/2 of (5(sin(x)-1))/(cos^2(x))

x \to \frac{π}{2} lim (\frac{5 ( sin ( x ) - 1 )}{cos ^{2} ( x )})

- \frac{5}{2}

Decimal

- 2.5

Solution steps

x \to \frac{π}{2} lim (\frac{5 ( sin ( x ) - 1 )}{cos ^{2} ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 5 \cdot x \to \frac{π}{2} lim (\frac{sin ( x ) - 1}{cos ^{2} ( x )})

Rewrite using trig identities

= 5 \cdot x \to \frac{π}{2} lim (- \frac{1}{1 + sin ( x )})

Plug in the value

x = \frac{π}{2}

= 5 (- \frac{1}{1 + sin ( \frac{π}{2} )})

Simplify

5 (- \frac{1}{1 + sin ( \frac{π}{2} )}) : - \frac{5}{2}

= - \frac{5}{2}

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What is the limit as x approaches pi/2 of (5(sin(x)-1))/(cos^2(x)) ?
The limit as x approaches pi/2 of (5(sin(x)-1))/(cos^2(x)) is -5/2