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

Question

Y RAJYALAKSHMI · Answer

tan 2 x – sec 10 x + 1 = 0 => sec 2 x – sec 10 x = 0 (as 1+ tan 2 x = sec 2 x) =>sec 2 x(1 – sec 8 x) = 0 =>sec 2 x(1 – secx)(1 + secx)(1 + sec 2 x)(1 + sec 4 x) = 0 => sec 2 x = 0, (1 – secx)= 0 , (1 + secx) = 0, (1 + sec 2 x)= 0, (1 + sec 4 x) = 0 The real roots are only for sec 2 x = 0, (1 – secx)= 0 , (1 + secx) = 0 sec 2 x = 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

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

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

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