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**Tweety** Given that $\displaystyle tan^{2}K = 2secK $

a) find the value of sec *k*.

(b) deduce that cos*k*=√2−1

$\displaystyle tan^{2}k = 2secK $

$\displaystyle sec^2k-1 = 2secK $

$\displaystyle sec^2K-2secK-1 = 0 $

$\displaystyle secK = 1+ \sqrt{2} $

b) $\displaystyle \frac{1}{cosk} = 1+\sqrt{2} $

$\displaystyle cosK = \frac{1}{1 + \sqrt{2}} $

I don't get the right answer, if I rationalise the denominator by multiplying top and bottom by $\displaystyle 1 - \sqrt{2} $ I still don't get $\displaystyle cosK = \sqrt{2} -1 $