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Question

If 3x = sec∅ and 3÷x = tan∅, then find the value of
(x^2-1÷x^2).

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Solution

3x = sec@ ---------- 1 3/x = tan@-----------2

x = sec@/3 1/x = tan@/3

x2 =sec2@/9 1/x2 = tan2@/9

x2 - 1/x2 =sec2@/9 - tan2@/9

= (sec2@ - tan2@) / 9

9( x2 - 1/x2 ) = 1 since sec2@ - tan2@ = 1 note : theta = @


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