Question

Question #3c38f

Answer 1

`cosec(A-B)=-5/4.`

Explanation:

`secA=-5/3 rArr color(green)(cosA=-3/5)` `:. sinA=sqrt(1-cos^2A)=sqrt(1-9/25)=+-4/5.`But `A in QII.` `:. color(red)(sinA=+4/5).`

`tanB=24/7.`:. `sec^2B=1+tan^2B=1+(24/7)^2=1+576/49=625/49.` `:. secB=+-25/7.`But `B in QIII. :. secB=-25/7, or, color(red)(cosB=-7/25).`

Now, `color(green)sinB=tanBcosB=24/7*(-7/25)=color(green)(-24/25).`

Now, `sin(A-B)=color(red)(sinAcosB)-color(green)(cosAsinB)=color(red)(4/5*(-7/25))-color(green)((-3/5)*(-24/25))=-28/125-72/125=-100/125=-4/5.`

Therefore,`cosec(A-B)=-5/4.`