Question

Compute sin 53°/cos 37° - 2.tan 45 + cosec 60°/ sec 30°

Answer 1

sin53/cos37 - 2tan45 + cosec60/sec30
=sin53/sin(90 - 37) - 2 + cosec60/cosec(90 - 30)        (tan 45 = 1)
=sin53/sin53 - 2 + cosec 60 / cosec60
=1 - 2 + 1
=0

Answer 2

sin53°/cos37° -2.tan45°+cosec60°/sec30°

we know,
sin@ =cos(90°-@)
so, sin53°=cos(90°-53) =cos37°
also,
cosec@= sec(90°-@)
cosec60°=sec(90°-60°) =sec30°

now,
sin53°/sin53°-2(1) +cosec60°/cosec60°

1 -2 +1 =0 (answer)