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find the number of the solutions of the equation in [0,360] tan(5pi.cos(A))=cot(5pi.sin(A))

find the number of the solutions of the equation in [0,360]
tan(5pi.cos(A))=cot(5pi.sin(A))

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
Given ques:tan(5 pi.cos A)=cot(5pi.sinA)=>tan(5pi.cosA)=tan(pi/2-(5pi.sinA)) =>5picos A=pi/2-5pi sinA
=>5cosA=1/2 -5sinA =>1/2=5cosA+5 sinA
=>1/2=5(cosA+sinA)=> ½=5sqrt2 (sin pi/4.cos A+cos pi/4.sinA)
=>1/2=5sqrt(2) sin(pi/4+A) =>1/(10 sqrt(2)) =sin(pi/4 +A)
In ques given interval: [0,2pi]. A=1/4(3pi-4 sin^-1(1/(10sqrt(2)))) and A=1/4(7pi-4 sin^+4(1/(10sqrt(2))))
 
So there are 2 solutions .
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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