trigo !!!!

e^{-Î 2}<Î¸<Î 2

the larger of cos(logÎ¸) and log(cosÎ¸) if e^{-Î 2}<Î¸<Î 2 is ____ ?

2 Answers

now log(cosÎ¸) will always be negative in the interval
{infact log(cosÎ¸)is always negative except when Î¸=0 when it becomes 0}

now for cos(logÎ¸) we notice that cos(log(e^{-Î /2})=0
and all the values after it will be positive till Î¸<Î /2

so cos(logÎ¸)>log(cosÎ¸)

for cos (log x) to exist. xmust be betn 0 and âˆ©/2.

taking that condn log x in that region is very close to 0. so cos(logx) is very close to 1.as cosine graph decreases from 1 to 0the interval 0-âˆ©/2.

cos x in the region is betn0-1.so log(cos x) is negative in the region as log of something betn 0 and 1 with base>1 is negative

so cos(log x)>log(cos x)

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