What is (sin(x)-1)(ln(sin(x))-ln(cos(x))) ?

The solution to (sin(x)-1)(ln(sin(x))-ln(cos(x))) is (sin(x)-1)ln(tan(x))

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simplify (sin(x)-1)(ln(sin(x))-ln(cos(x)))

simplify

(sin (x) - 1) (ln (sin (x)) - ln (cos (x)))

(sin (x) - 1) ln (tan (x))

Solution steps

(sin (x) - 1) (ln (sin (x)) - ln (cos (x)))

Apply log rule:

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

ln (sin (x)) - ln (cos (x)) = ln (\frac{sin ( x )}{cos ( x )})

= ln (\frac{sin ( x )}{cos ( x )}) (sin (x) - 1)

Rewrite using trig identities

= (sin (x) - 1) ln (tan (x))

\frac{5}{9} lo g_{2} (3)

5 lo g_{7} (11) - lo g_{7} (3)

ln (956 \cdot 178108)

- ln (- 2 x)

ln (\frac{2 ^{2} + 1}{2 ( 2 ) ^{2} + 1})

What is (sin(x)-1)(ln(sin(x))-ln(cos(x))) ?
The solution to (sin(x)-1)(ln(sin(x))-ln(cos(x))) is (sin(x)-1)ln(tan(x))