Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
the number of distinct real roos of the equation tan 2 2x+2tan2xtan3x-1=0 in the interval(0,90)
6simply put tan^x=ywe 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 0let f(y)= 7y^3-35y^2+21y-1now 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
simply put tan^2x=ywe 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 0let f(y)= 7y^3-35y^2+21y-1now 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 infinityso the given equation has 3 real roots
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -