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The abscissas of point Pa n dQ on the cu...

The abscissas of point `Pa n dQ` on the curve `y=e^x+e^(-x)` such that tangents at `Pa n dQ` make `60^0` with the x-axis are. `1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2)` `1n((sqrt(3)+sqrt(7))/2)` (c) `1n((sqrt(7)-sqrt(3))/2)` `+-1n((sqrt(3)+sqrt(7))/2)`

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The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. )a) 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) (d) +-1n((sqrt(3)+sqrt(7))/2)

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

1/(sqrt(7)+sqrt(3))\times (sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3))

Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-1/(sqrt(6)-\ sqrt(5))+1/(sqrt(5)-2)=5

Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

Evaluate : (1)/(3-sqrt(8)) -(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2).

Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2) then-

The sum n terms of the series 1/(sqrt(1)+sqrt(3))+1/(sqrt(3)+sqrt(5))+1/(sqrt(5)+sqrt(7))+ is sqrt(2n+1) (b) 1/2sqrt(2n+1) (c) 1/2sqrt(2n+1)-1 (d) 1/2{sqrt(2n+1)-1}