Question

if cos (a+b)=0 andcot (a-b)=root 3. find sec a tan b - cot a sin b

$\sqrt{3}$
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Answer 1

Answer:

Step-by-step explanation:

cos(a+b)=0

cos90=0

⇒a+b=90      ---1    

cot(a-b)=$\sqrt{3}$

cot30=$\sqrt{3}$

⇒a-b=30       ---2

1+2= a=60

∴b=30

sec60=2

tan30=$\frac{1}{\sqrt{3}}$

cot60=1/rt3

sin30=1/2

=$\frac{2}{\sqrt{3}}-\frac{1}{\sqrt{3}}$×$\frac{1}{2}$

=$\frac{4-1}{\sqrt3*2}$

=$\frac{\sqrt{3}}{2}$ (after rationalization)

=cos30/sin60