Answer to Question #11152 in Trigonometry for see

Question

find the values of √sinθ cosθ/secθ cscθ given that tan=3/4 and θ is an acute angle.

Answer 1

Since θ is an acute angle, sinθ>0 and cosθ>0.
Then from tanθ=3/4 we get
that

sinθ = 3 / sqrt(3^2+4^2) = 3/5
cosθ = 4 / sqrt(3^2+4^2) =
4/5

Hence

secθ = 1/cosθ = 5/4
cscθ = 1/sinθ =
5/3

Therefore
sqrt(sinθ cosθ/secθ cscθ) =
= sqrt( (3/5 * 4/5)
/ (5/4 * 5/3) )
= sqrt( (3/5 * 4/5) * (3/5 * 4/5) )
= 3/5 *
4/5
= 12/25