Question

If 2x =sec a and 2/x =tan a , prove that x2-1/x2=1/4 x

Answer 1

correction:- prove that, 2x²-2/x² = 1/4

Step-by-step explanation:

Given

2x = sec A

=> x = secA /2...........(1)

2/x = tan A

=> 1/x = tanA /2...........(2)

To prove

x²-1/x² = 1/4

LHS

= x²-1/x²

=( secA /2)²-(tanA /2)²

= (1/4) (sec²A-tan²A)

= 1/4

= RHS

HENCE PROVED

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