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Find theta such that (3+2i sin theta)/(1...

Find `theta` such that `(3+2i sin theta)/(1-2i sin theta)` is purely real.

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Prove that : sin 2 theta= 2sin theta cos theta .

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

If x = 2 cos theta - cos 2 theta, y = 2 sin theta - sin 2 theta, find dy/dx at theta = pi/2

If p tan theta = tan p theta , then show that : (sin^2 p theta)/(sin^2 theta)= (sin p^2)/(1+(p^2-1)sin^2 theta) .

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

Let f_(n)(theta)= 2 sin . (theta)/(2) sin. (3theta)/(2) + 2 sin.(theta)/(2) sin. (5theta)/(2) + 2sin. (theta)/(2) sin. (7 theta)/(2) + ... + 2 sin (2 n+1) (theta)/(2), n in N , then which of the following is/are correct ?

Prove by Principle of Mathematical Induction, that : sin theta + sin 2 theta + sin 3 theta + ........ + sin n theta= (sin (n+1)theta/2 sin frac (n theta)(2))/(sin frac (theta)(2)) for all n in N.

Prove the following identity : (cot^2 theta)/((1- cosec theta)^2)= (1+sin theta)/(1-sin theta) .

JBD PUBLICATION-MODEL PAPER (15)-EXERCISE
  1. Prove that A^c-B^c=B-A.

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  2. If f(x)=log(x/(x-1)), show that f(x+1)+f(x)=log ((x+1)/(x-1))

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  3. Prove that:cos15^@-sin15^@=1/sqrt2

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  4. Prove that : cos 24^@+ cos 55^@ + cos 125^@ + cos204^@ + cos 300^@= 1/...

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  5. How many words, with or without meaning, each of 2 vowels and 3 conson...

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  6. Find the value of n such that : "^nP5=42 ^nP3, n>4.

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  7. Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove...

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  8. If the angle between two lines is pi/3 and slope of one of the line is...

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  9. If a parabolic reflector is 20 cm in diameter and 50 cm deep. Find the...

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  10. Evaluate: underset(xrarr1)lim ((x+x^2+x^3+……….x^n)-n)/(x-1)

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  11. If y=asinx+bcosx, prove thaty^2+((dy)/(dx))^2=a^2+b^2

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  12. A,B and C are three mutually exclusive and exhaustive events associat...

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  13. Find theta such that (3+2i sin theta)/(1-2i sin theta) is purely real.

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  14. If a + ib = ((x+i)^2)/(2x^2+1), prove that a^2+b^2 =((x^2+1)^2)/((2x^2...

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  15. Solve the following system of inequalities graphically: 4x + 3y le 60,...

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  16. IQ of a person is given by the formula IQ= (MA)/(CA)xx100 , where MA i...

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  17. Evaluate: underset(xrarr0)lim (sqrt(1+2x)-sqrt(1-2x))/(x)

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  18. Find the derivative of cos x w.r.t. x

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  19. Find the mean marks from the following data :

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  20. Find the mean deviation from the mean for the following data. 38, 70, ...

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