Question

❤.......hey
find the value of cos 38 ° cosec 52° / tan18° tan 35° tan 60° tan 72° tan 55° .

Answer 1

We know that :

✿  Sinθ × Cosecθ = 1

✿ Tanθ × Cotθ = 1

✿ Cos38° = Cos(90 - 52)° = Sin52°

✿ Tan18° = Tan(90 - 72)° = Cot72°

✿ Tan35° = Tan(90 - 55)° = Cot55°

$\bf{\implies \dfrac{Cos(38) \times Cosec(52) }{Tan(18) \times Tan(35) \times Tan(60) \times Tan(72) \times Tan(55)}}$

$\bf{\implies \dfrac{Sin(52) \times Cosec(52) }{Cot(72) \times Cot(55) \times Tan(60) \times Tan(72) \times Tan(55)}}$

$\bf{\implies \dfrac{[Sin(52) \times Cosec(52)]}{[Cot(72) \times Tan(72)] \times Tan(60) \times [Cot(55) \times Tan(55)]}}$

$\bf{\implies \dfrac{[1]}{[1] \times Tan(60) \times [1]}}$

$\bf{\implies \dfrac{1}{\sqrt{3}}$

Answer 2

$your \: answer$
remember some identity

cos(90-A)=sinA

tan(90-A)=cot A

so here

cos 38° = cos(90-52)=sin52°

tan18°=tan(90-72)=cot 18°

same way

tan35°=tan(90-55)=cot 55°

now put values

sin52°×cosec52°/ cot 72°×cot55°×tan60°×tan72°×tan55°

now we know

tan =1/cot

cosec=1/sin

tan60°=√3

and vice versa

so

final answer will be

1/tan60° =1/√3

hope helps