Prove that cosec 60 degrees cot 30 degrees tan 60 degrees=2secsquared 45degrees cos 30 degree

Answer 1

Work on the left-hand side first:
csc60 cot30 tan60
=(1/sin60)(tan60)(tan60)
=(1/sin60)(tan²60)
=(1/sin60)(sec²60-1)
=(2/√3)(2²-1)
=2√3

Work on the right-hand side:
2sec²45cos30
=2(2/√2)² (√3)/2
=8/2 (√3)/2
=2√3

Thus LHS=RHS and the proof is complete.

Answer 2

csc60° * cot 30° * tan 60°
= 2/√3 * √3 * √3
= 2√3

2sec^2 45° cos30°
= 2*2*√3/2
= 2√3