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By using properties of determinats. Prov...

By using properties of determinats. Prove that-
`|(sintheta,costheta,sin2theta),(sin(theta+(2pi)/3), cos(theta + (2pi)/3) ,sin(2theta + (4pi)/3)),(sin(theta-(2pi)/3) ,cos(theta - (2pi)/3), sin (2theta - (4pi)/3))|= 0`

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Prove that for all values of theta , |{:(sintheta,costheta,sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2pi)/(3)),sin(2theta+(4pi)/(3))),(sin(theta-(2pi)/(3)),cos(theta-(2pi)/(3)),sin(2theta-(4pi)/(3))):}|=0

Prove that (cos2theta)/(1+sin2theta)=tan(pi/4-theta) .

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that, cos^(3) theta cos 3 theta + sin^(3) theta sin 3 theta = cos^(3) 2 theta

Prove that, (sin 3 theta)/(sin theta)-(cos 3 theta)/(cos theta)=2

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Prove that (sin 3theta-sintheta)/(costheta-cos3 theta)=cot2 theta

Prove that 4 sin theta sin(pi/3 + theta) sin (pi/3-theta) = sin 3 theta

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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. By using properties of determinats. Prove that- |(x+4,2x,2x),(2x,x+4...

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  2. By using properties of determinats. Prove that- |(1,1+x,1+x+y),(2,3+...

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  3. By using properties of determinats. Prove that- |(sintheta,costheta,...

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  4. Let X = [(3,2,5),(4,1,3),(0,6,-7):}] express X as sum of two matrics s...

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  5. If [(2,-1),(1,0),(-3,4):}]xxP= [(-1,-8,-10),(1,-2,-5),(9,22,15):}], fi...

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  6. Prove that: underset(xrarrinfty)lim sqrtx (sqrt(x+3) - sqrtx)= 3/2

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  7. Prove that:underset(x rarr0)lim ((x-1+cosx)/(x))^(1/x) = e^(-1/2)

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  8. Prove that: underset(xrarrinfty)lim ((x+5)/(x+1))^x = e^4

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  9. Prove that: underset(xrarrpi/2)lim (1+cosx)^(3secx) = e^3

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  10. Prove that: underset(xrarr0)lim ([1+3x]^((x+3)/x))= e^9

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  11. Evaluate the following limits: underset(x rarr0)lim(xe^x - log(x+1))/(...

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  12. Evaluate the following limits: underset(x rarr0)lim[tan(pi/4+x)]^(1/x)

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  13. Evaluate the following limits: underset(x rarr0)lim(sinx + cos x)^(1/x...

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  14. Evaluate the following limits: underset(x rarr0)limsinlog(1+x)/log(sin...

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  15. It g(x) is the inverse of f(x) and f(X) = (1+x^3)^-1, show that g'(x) ...

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  16. Find the differential coefficients of the folloiwng functions: x^x

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  17. Find form 1st principle the differential coefficients of the folloiwng...

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  18. Find form 1st principle the differential coefficients of the folloiwng...

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  19. Find dy/dx when x^(siny) + y ^(sinx) = 1

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  20. Find dy/dx when x^(logx) + (sinx)^x + 15 x

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