What is ln(tan(1/2)θ[ 1/(1+cos(θ))]) ?

The solution to ln(tan(1/2)θ[ 1/(1+cos(θ))]) is ln(tan(1/2))+ln(θ)++ln(1)-ln(1+cos(θ))

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simplify ln(tan(1/2)θ[ 1/(1+cos(θ))])

simplify

ln (tan (\frac{1}{2}) θ [\frac{1}{1 + cos ( θ )}])

ln (tan (\frac{1}{2})) + ln (θ) + + ln (1) - ln (1 + cos (θ))

Solution steps

ln (tan (\frac{1}{2}) θ [\frac{1}{1 + cos ( θ )}])

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (tan (\frac{1}{2}) θ [\frac{1}{1 + cos ( θ )}]) = ln (tan (\frac{1}{2})) + ln (θ) + ln (\frac{1}{1 + cos ( θ )})

= ln (tan (\frac{1}{2})) + ln (θ) + ln (\frac{1}{cos ( θ ) + 1})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{1 + cos ( θ )}) = ln (1) - ln (1 + cos (θ))

= ln (tan (\frac{1}{2})) + ln (θ) + + ln (1) - ln (cos (θ) + 1)

\frac{ln ( 60000 ) - ln ( 100 )}{ln ( 75000 ) - ln ( 100 )}

ln (a \cdot x^{a})

ln (\frac{( a ^{3} b ^{5} )}{6 c})

lo g_{4} (x^{4}) y

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

What is ln(tan(1/2)θ[ 1/(1+cos(θ))]) ?
The solution to ln(tan(1/2)θ[ 1/(1+cos(θ))]) is ln(tan(1/2))+ln(θ)++ln(1)-ln(1+cos(θ))