What is the value of $\frac{sin33°cos57°+sec62°sin28°+cos33°sin57°+cosec62°cos28°}{tan15°tan35°tan60°tan55°tan75°}$ ?

$\sqrt{3}$

Using ,

sinA = cosB   ( A + B = 90° )

& tanA × tanB = 1  ( A + B = 90° ) 

$\frac{sin33°cos57°+sec62°sin28°+cos33°sin57°+cosec62°cos28°}{tan15°tan35°tan60°tan55°tan75°}$

= $\frac{sin33°sin33°+sec62°cos62°+cos33°cos33°+cosec62°sin62°}{tan15° ×tan75°tan35°×tan55°×√3 }$ 

= $\frac{1+1+1}{√3 }$

= $\frac{3}{√3 }$

= √3