The number of solutions of the equa...
Question
Fullscreen

The number of solutions of the equation tanx - sec 10x + 1 - 0 in (0.10) is - (A) / (B) 6 (C) 10 (D) 11 al

JEE/Engineering Exams
Maths
Solution
127
Rating
4.0 (1 ratings)
Fullscreen
( tan ^{2} x-sec ^{10} x+1=0 ) ( Rightarrow sec ^{2} x-sec ^{10} x=0 quadleft(operatorname{as} 1+tan ^{2} x=sec ^{2} xright) ) ( Rightarrow>sec ^{2} xleft(1-sec ^{8} xright)=0 ) ( Rightarrow>sec ^{2} x(1-sec x)(1+sec x)left(1+sec ^{2} xright)left(1+sec ^{4} xright) ) ( =0 ) ( Rightarrow sec ^{2} x=0,(1-sec x)=0,(1+sec x)=0,(1+ ) ( left.sec ^{2} xright)=0,left(1+sec ^{4} xright)=0 ) The real roots are only for sec ( ^{2} x=0,(1-sec x)= ) ( 0,(1+sec x)=0 ) ( sec ^{2} x=0 Rightarrow sec x=0 ) ( (1-sec x)=0 Rightarrow sec x=1 ) ( (1+sec x)=0 Rightarrow sec x=-1 ) only one solution secx ( =1 ) is in the interval (0, 10) Ans ( =1 )
Quick and Stepwise Solutions Just click and Send Download App OVER 20 LAKH QUESTIONS ANSWERED Download App for Free