Flag Trigonometry> no. of solutions of the equation tan^2x-s...
question mark

no. of solutions of the equation tan^2x-sec^10x+1=0 in (0,10) ?

manvi makkar , 10 Years ago
Grade
anser 1 Answers
Y RAJYALAKSHMI

Last Activity: 10 Years ago

tan2x – sec10x + 1 = 0
=> sec2x  – sec10x = 0  (as 1+ tan2x = sec2x)
=>sec2x(1 – sec8x) = 0
=>sec2x(1 – secx)(1 + secx)(1 + sec2x)(1 + sec4x) = 0
=> sec2x = 0, (1 – secx)= 0 , (1 + secx) = 0, (1 + sec2x)= 0, (1 + sec4x) = 0
The real roots are only for sec2x = 0, (1 – secx)= 0 , (1 + secx) = 0
sec2x = 0 => secx = 0
(1 – secx)= 0 =>  secx = 1
(1 + secx) = 0 => secx = – 1
only one solution secx = 1 is in the interval (0, 10) 
Ans = 1
 

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments