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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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  • ANNUAL EXAMINATION QUESTION PAPERS 2015

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If 2n alpha= pi/2, then show that tan alpha tan 2 alpha tan 3 alpha.... Tan (2n-2) alpha tan (2n-1) alpha=1

Show that, (x tan alpha + y cot alpha)( x cot alpha + y tan alpha) = (x+y)^(2) + 4 xycot^(2) 2 alpha.

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

The value of tanalpha+2tan(2alpha)+4tan(4alpha)+...+2^(n-1)tan(2^(n-1)alpha)+2^(n)cot(2^(n)alpha) is

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

If tanalpha=1/7 ,sinbeta=1/sqrt10 prove that alpha+2beta=(pi/4) where 0ltalphaltpi/2 and 0ltbetalt(pi//2)

UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2016-EXERCISE
  1. If f(x)=e^(px+q),then shoq that f(a).f(b).f(c)=f(a+b+c).e^(2q)

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  2. if 13theta=pi,then show that cos3theta+cos5theta+2costheta.cos9theta=0

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

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  4. Find the square root of i

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  5. Find the (r+1)th term from the end in the expansion of (1-3x)^n.

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  6. Prove that by using the principle of mathematical induction for all n...

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  7. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3 , respectiv...

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  8. Find the locus of the mid-point of the portion of the line x cosalpha+...

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  9. If the coordinates of a point lies on the ellipse 9x^2+16y^2=144 be (2...

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  10. If y=e^x/(1+x^2),determin dy/dx.

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  11. Evaluate :lim(xrarrpi/4)(1-tanx)/(x-pi/4)

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  12. can 7/2be the probability of an event? Explain.

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  13. Two variables x and y are related by y=10-3x.If the standard deviation...

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  14. For any three sets A,B and C prove that Acup(BcapC)=(AcupB)cap(AcupC)

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  15. Find the value of 16cos(pi/15).cos((2pi)/15).cos((4pi)/15).cos((8pi)/1...

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  16. Show that sin^3alpha+sin^3(120^@+alpha)+sin^3(240^@+alpha)=-3/4sin3alp...

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  17. Prove that by using the principle of mathematical induction for all n...

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  18. If the P^(th)and q^(th)terms of an A.Pare a and b respectively,then sh...

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  19. Find the probability of drawing 4 cards from a pack of 52 cards such t...

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  20. Find the sum of n-terms of the following series:(x+1/x)^2+(x^2+1/x^2)^...

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