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Show that secalpha-tanalpha=cot(pi/4+alp...

Show that `secalpha-tanalpha=cot(pi/4+alpha/2)`

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Which of the following identities, wherever defined, hold(s) good? (a)cotalpha-tanalpha=2cot2alpha (b)tan(45^0+alpha)-tan(45^0-alpha)=2cos e c2alpha (c)tan(45^0+alpha)+tan(45^0-alpha)=2sec2alpha (d)tanalpha+cotalpha=2tan2alpha

(sqrt2-sinalpha-cosalpha)/(sinalpha-cosalpha) is equal to (a) sec(alpha/2-pi/8) (b) cos(pi/8-alpha/2) (c) tan(alpha/2-pi/8) (d) cot(alpha/2-pi/2)

If tan alpha+cotalpha=2, show that, tan^7alpha+cot^7alpha=2.

Prove the following identities: (sinalpha+cosecalpha)^2+(cosalpha+secalpha)^2=tan^2alpha+cot^2alpha+7

If cot^3alpha+cot^2alpha+cotalpha=1 then (a) cos2alpha.tanalpha=-1 (b) cos2alpha.tanalpha=1 (c) cos2alpha-tan2alpha=1 (d) cos2alpha-tan2alpha=-1

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If cosec theta+sectheta=cosecalpha+secalpha ,then show that tan ((theta+alpha)/2)=cotthetacotalpha

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UNITED BOOK HOUSE-MCQ-EXERCISE
  1. If cosalpha+cosbeta=1/3and sinalpha+sinbeta=1/4,show that tan ((alpha+...

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  2. Show that 1/(sin10^@)-sqrt3/(cos10^@)=4

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  3. Show that secalpha-tanalpha=cot(pi/4+alpha/2)

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  4. Solve :3sin^2x+7cos^2x=6

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  5. In triangleABC angleB=60^(@), c=2sqrt(3), b =3sqrt(2) then find angle...

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  6. If (2^(2n)-1)is divisible by 3, then show that [2^(2(n+1))-1]is also d...

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  7. Simplify : (1+i)^(-2)-(1-i)^(-2)

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  8. Find a quadratic equation with rational co-efficient whose one root is...

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  9. State fundamental theorem of algebra

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  10. If ^9P5 + 5. ^9P4 = ^I0Pr, find r.

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  11. If ^nC4=21xx^(n//2)C3find n.

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  12. Find the middle term (or terms) in the following expansions: (iii) (...

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  13. The sum to n terms of an A.P. is n^(2). Find the common difference.

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  14. If the slope of the line joining the points (2k,-2) and (1,-k) be (-2)...

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  15. Find the equation to the circle whose parametric equations are, x = ...

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  16. Find the equation- of the porabola whose co-ordinates of the vertex an...

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  17. Find the the co-ordinates of the point on the ellipse x^2 + 2y^2 =4 wh...

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  18. Show that the eccentricities of the two hyperbolas x^2/16-y^2/9=1and x...

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  19. Find the co-ordinates of the point of trisection of the line segment j...

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  20. show that lim(nrarr0)(root(3)(n+1)-1)/n=1/3

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