(1+sinθ)/cosθ = x sinθ/cosθ + 1/cosθ = x tanθ + secθ = x ...........................(i) secθ = x – tanθ On squaring both sides, (secθ)2 = (x-tanθ)² sec²θ = x²+ tan²θ-2xtanθ sec²θ-tan²θ = x² -2xtanθ 1 = x² -2xtanθ tanθ = (x²-1)/2x Now putting the value of tanθ in equation (i) (x²-1)/2x + secθ = x secθ = x - (x²-1)/2x secθ = (2x²-x²+1)/2x = (x2+ 1)/2x Alternate method: (1+sinθ)/cosθ = x sinθ/cosθ + 1/cosθ = x tanθ + secθ = x secθ+tanθ = x ...........................(i) So secθ-tanθ = 1/x ...........................(ii) {As sec2θ - tan2 θ = 1 } Adding both equations 2secθ = x + 1/x = (x2+1)/x So secθ = (x2+1)/2x
640 322 164 86 48 ?
...18 22 49 ? 190 226
...542 541 532 507 458 ?
...219 365 511 ? 803 949
...To find the Next number in the given series.
342 510 726 996 1326 ?
...102, 246, 442, 698, 1022, ?
6 , 21, 116, ?, 4674, 33593
83, 88, 86, 91, 89, ?
2, 17, 147, 1167, 8157, 48957
34, 18, 20, ?, 70, 180
