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

  • Math -

    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.

  • Math -

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

    2sec^2 45° cos30°
    = 2*2*√3/2
    = 2√3

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