What is the value of -5cos(pi/4)(1+ln(10sin(pi/4))) ?

The value of -5cos(pi/4)(1+ln(10sin(pi/4))) is -(5sqrt(2)(1+ln(5)+1/2 ln(2)))/2

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-5cos(pi/4)(1+ln(10sin(pi/4)))

- 5 cos (\frac{π}{4}) (1 + ln (10 sin (\frac{π}{4})))

- \frac{5 2 ( 1 + ln ( 5 ) + \frac{1}{2} ln ( 2 ) )}{2}

Solution steps

- 5 cos (\frac{π}{4}) (1 + ln (10 sin (\frac{π}{4})))

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

= - 5 \cdot \frac{2}{2} (1 + ln (10 \cdot \frac{2}{2}))

Simplify

- 5 \cdot \frac{2}{2} (1 + ln (10 \cdot \frac{2}{2})) : - \frac{5 2 ( 1 + ln ( 5 ) + \frac{1}{2} ln ( 2 ) )}{2}

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

cos (\frac{π ^{1}}{2}) \frac{π}{2}

tan (\frac{11 π}{6} - \frac{5 π}{4})

8 \cdot sin (5 0^{\circ})

2 sin (5 0^{\circ})

2 sin (2 5^{\circ}) cos (2 5^{\circ})

What is the value of -5cos(pi/4)(1+ln(10sin(pi/4))) ?
The value of -5cos(pi/4)(1+ln(10sin(pi/4))) is -(5sqrt(2)(1+ln(5)+1/2 ln(2)))/2