SOLUTION: If 0 < x < 90 and {{{ cos x = 3/sqrt (10) }}}, compute log(sinx)+log(cosx)+log(tanx).

Question 1112843: If 0 < x < 90 and , compute log(sinx)+log(cosx)+log(tanx).
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Given . Hence, , , and

The rest is just calculator work. I'll leave that to your capable fingers.

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

log(sinx)+log(cosx)+log(tanx) = log(sinx*cosx*tanx) = log((sinx)^2)

If the angle is in quadrant I and cosx = 3/sqrt(10), then sinx = 1/sqrt(10).

Then log((sinx)^2) = log(1/10) = -1.
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