Question

Prove that 2/3 cosec square 58 - 2/3 cot 58 tan 32 - 5/3 tan 13 tan 37 tan 45 tan 53 tab 37 = -1

Answer 1

It is tan 53 not tan 13.
2/3cosec^2 58 - 2/3cot58·tan32 - 5/3 tan53·tan37·tan45·tan53·tan37= -1
L.H.S
2/3cosec^2 58 - 2/3cot58·tan32 - 5/3 tan53·tan37·tan45·tan53·tan37
2/3cosec^2 58 - 2/3cot58·tan(90-32) - 5/3 tan(90-53)·tan37·tan45·tan(90-53)·tan37                                                            {By complementary angles}
2/3cosec^2 58 - 2/3cot58·cot58 - 5/3 cot37·tan37·tan45·cot37·tan37
2/3cosec^2 58 - 2/3cot^2 58 - 5/3 1/tan37·tan37·tan45·1/tan37·tan37 {cotΘ=1/tanΘ}
2/3[cosec^2 58 - cot^2 58] - 5/3 ·tan45
2/3[1] - 5/3 ·1                       {cosec^2Θ-cot^2Θ=1 ; tan45=1}
2/3-5/3
-3/3 = -1
Therefore L.H.S=R.H.S
So 2/3cosec^2 58 - 2/3cot58·tan32 - 5/3 tan53·tan37·tan45·tan53·tan37= -1

Answer 2

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