Answer:
-31/17
Step-by-step explanation:
csc²α-cot²α=1
cot²α=csc²α-1=(25/7)²-1=(625-49)/49=576/49
α is in 2nd quadrant so cotα is negative.
cot α=-√(576/49)=-24/7
tan α=-7/24
cos β=√2/2
sec β=2/√2=√2
sec²β-tan ²β=1
tan ²β=sec²β-1
tan²β=(√2)²-1=2-1=1
β is in 1st quadrant ,so tan β is positive.
tan β=1
[tex]tan (\alpha -\beta )=\frac{tan \alpha -tan \beta }{1+tan \alpha tan \beta } \\=\frac{\frac{-7}{24} -1}{1+(\frac{-7}{24}) (1)} \\=\frac{-7-24}{24-7} \\=\frac{-31}{17}[/tex]
