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If.y = tan^-1 (sec x + tan x), show that...

If.y = `tan^-1 (sec x + tan x)`, show that ,`dy/dx=1/2` .

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 5-EXERCISE
  1. Find the ratio in which the straight line 3x + y = 9 divides the line ...

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  2. Prove that: lim(xrarr0)tanx/x=1

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  3. If.y = tan^-1 (sec x + tan x), show that ,dy/dx=1/2 .

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  4. A and B are two independent event. It P(A) = 1/2 and P(A cup B)=2/3,fi...

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  5. Find the mean deviation with respect ' to mean value :18,22,33,42,53,...

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  6. Find the HCF of 15, 40, 60 with the help of set theory

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  7. If 13theta=pi,show that costhetacos2theta cos3theta cos4theta cos5thet...

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  8. Solve:sinx-sin2x=cos2x-cosx

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  9. Show that by mathematical- induction :x^3+(x+1)^3+(x+2)^3is divisible ...

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  10. If z = x + iy and arg ((z-1)/(z+1))=(pi)/(4), then the locus of (x, y)...

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  11. If the co-efficient of the (3r+1) th term is equal to the co-efficient...

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  12. Find the sum of 1 + 5 + 12 + 22 + 35 +….upto n term.

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  13. A straight line passes through A(1, 2) and makes an angle theta with t...

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  14. Find the equations of the lines, which cut-off intercepts on the axes ...

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  15. The equation of circum circle of an equilateral triangle is x^2+y^2+2g...

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  16. A straight line passes through (h, k) and the middle point of the also...

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  17. Evaluate :lim(xrarr0)(tan2x-x)/(3x-sinx)

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  18. From definition, differentiate cos4x at 'x=pi/6,will respect to x.

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  19. Prove the following by contradiciton ."The sum of a rational and an ir...

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  20. Show that sqrt7 is an irrational, (use the method of contradiction)

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