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Grade: 10

                        

the number of distinct real roos of the equation tan 2 2x+2tan2xtan3x-1=0 in the interval(0,90)

2 years ago

Answers : (2)

Aditya Gupta
2056 Points
							
6simply put tan^x=y
we also know that tan2x=2tanx/(1-tan^2x) and tan3x= (3tanx-tan^3x)/(1-3tan^2x)
so putting al these in the given equation, and removing the denominators with simmplification gives:
7y^3-35y^2+21y-1=0 (Note that 0
let f(y)= 7y^3-35y^2+21y-1
now we see that f(0)*f(1/3)
also, f(1/3)*f(1)
and since f(1)
so the given equation has 3 real roots
2 years ago
Aditya Gupta
2056 Points
							
 
simply put tan^2x=y
we also know that tan2x=2tanx/(1-tan^2x) and tan3x= (3tanx-tan^3x)/(1-3tan^2x)
so putting all these in the given equation, and removing the denominators with simmplification gives:
7y^3-35y^2+21y-1=0 (Note that 0
let f(y)= 7y^3-35y^2+21y-1
now we see that f(0)*f(1/3)
also, f(1/3)*f(1)
and since f(1) is negative, one root also lies between 1 and infinity
so the given equation has 3 real roots
2 years ago
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