Question #3c38f

1 Answer
Ratnaker Mehta
Jun 16, 2016

#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.#

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