Alg9.4.38

Find the value of $\log_{10} \tan(40)\log_{10} \tan(41).......\log_{10} \tan(50)\,$

$\log_{10} \tan(40)\log_{10} \tan(41)..........\log_{10} \tan(45)........\log_{10} \tan(50)\,$

We know the value of tan45=1 Substituting the value in the give,

$\log_{10} \tan(40)\log_{10} \tan(41)..........\log_{10} 1........\log_{10} \tan(50)\,$

Logarithm of 1 is zero,

Hence

$\log_{10} \tan(40)\log_{10} \tan(41)..........(0)........\log_{10} \tan(50)\,$

Now the total value is zero.

Hence the solution is zero.