Question

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Answer 1

Secx =1/cosx =1/⅓=3

sen²x=8/9

senx= √8/√9 = 2√2/3

Cossecx =1/senx = 3/2√2 =3√2/4

Cotg²x=1/8

cotgx=√1/√8 =1/2√2 =√2/4

$\frac{ \sec(x) - \csc(x) }{1 - \cot(x) } = \frac{3 - \frac{3 \sqrt{2} }{4} }{1 - \frac{ \sqrt{2} }{4} }$

$= \frac{ \frac{12 - 3 \sqrt{2} }{4} }{ \frac{4 - \sqrt{2} }{4} } = \frac{12 - 3 \sqrt{2} }{4 - \sqrt{2} }$

$\frac{(12 - 3 \sqrt{2})(4 + \sqrt{2}) }{(4 - \sqrt{2} )(4 + \sqrt{2}) } = \frac{48 + 12 \sqrt{2} - 12 \sqrt{2} - 6}{16 - 2}$

$\frac{42}{14} = 3$

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