Question

Cos58/sin32-root3cos38cosec52/tan15tan60 tan75

Answer 1

Ans. 0

$\frac{ \cos(58) }{ \sin(90 - 58) } - \frac{ \sqrt{3 } \cos(38) \ \csc (90 - 38) }{ \tan(90 - 75) \tan(60) \tan(75) }$
We know that Sin(90-x)=Cosx
Cosec(90-x) = Secx
Tan (90-x) = Cotx
$\frac{ \cos(58) }{ \cos(58) } - \frac{ \sqrt{3 } \cos(38) \sec(38) }{ \ \cot(75) \sqrt{3} \tan(75) }$
Using, Cosx × Secx =1
and Cotx × Tanx =1
$1 - \frac{ \sqrt{3} }{ \sqrt{3} }$
= 0

Hope that helps.

Yours Truly
Yumieo