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If 5tanA=root7 where pi greater than less than 3pi/2 and secB=root11 where 3pi/2greater than B less than 2pi find the value of cosecA-tanB

If 5tanA=root7 where pi greater than less than 3pi/2 and secB=root11 where 3pi/2greater than B less than 2pi find the value of cosecA-tanB

Grade:11

1 Answers

sonika p
129 Points
6 years ago
Angle A lies in 3rd quadrant while angle B lies in 4th quadrant. 
5tanA = root7
tanA=root(7/5)
cosec^2 A – cot^2 A = 1
cosec^2 A = (25/7) + 1 = 32/7
cosec A = +/- root (32/7)
since A is in third quadrant and cosec is negative 
therefore, cosec A = – root(32/7)
secB = root(11)
sec^2 B – tan^2 B = 1
tan^2 B = 11-1 = 10
tan B = +/- root (10)
since B is in fourth quadrant and tan is negative 
therefore, tan B = – root(10)
cosec A – tanB = – root(32/7) +root(10)

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