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Simplify : cos theta[[costheta,si ntheta...

Simplify : `cos theta``[[costheta,si ntheta],[-si ntheta,costheta]]+si ntheta[[si ntheta,-costheta],[costheta,si ntheta]]`

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Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

costheta[{:(costheta,-sin theta),(sintheta,costheta):}]+sintheta[{:(sintheta,costheta),(-costheta,sintheta):}]=?

costheta-cos2theta=sin3theta

Simplify (1-costheta)/sintheta

Simplify (1-costheta)/sintheta

Solve: cos3theta+costheta=0

If A=[(cos theta, sin theta),(-sin theta, cos theta)] , then prove that A^n=[[cosntheta,sin ntheta],[-sin ntheta,cos ntheta]], n in N

Evaluate the determinates abs([-costheta,-sin theta],[sintheta,-costheta])

cos2 theta+2 costheta is always

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Evaluate: int0^1 1/(1+x^2)\ dx

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  2. Write the principal value of cos^(-1)(1/2)-2sin^(-1)(-1/2)

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  3. Simplify : cos theta[[costheta,si ntheta],[-si ntheta,costheta]]+si nt...

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  4. Evaluate int1^4(x^2-\ x)\ dx as a limit of sums.

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  5. If Delta=|[5, 3 ,8],[ 2, 0 ,1],[ 1 ,2 ,3]| , write the minor of the el...

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  6. Evaluate : int(1-x)sqrt(x)\ dxdot

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  7. Evaluate: int0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  8. Find lambda where projection of vec (a) = lambda hat (i) + hat (j) ...

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  9. If a line has direction ratios 2, –1, –2, then what are its directi...

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  10. Write the vector equation of the line given by (x-5)/3=(y+4)/7=(z-6...

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  11. Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4...

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  12. Using properties of determinants, solve the following for x: |[x-2, ...

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  13. If x=tan(1/alogy)\ , show that (1-x^2)(d^2\ y)/(dx^2)+(2x-a)(dy)/(dx)=...

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  14. Evaluate: int0^(pi/2)(x+sinx)/(1+cosx)

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  15. Solve the following differential equation: x\ dy-y\ dx=sqrt(x^2+y^2...

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  16. Solve the following differential equation: (y+3x^2)(dx)/(dy)=x

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  17. A speaks truth in 60% and Bin 80% of the cases. In what percentage of ...

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  18. If vec a and vec b are two vectors such that | vec a+ vec b|=| vec a...

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  19. In answering a question on a multiple choice test, a student either...

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  20. An urn contains 4 white and 3 red balls. Let X be the number of red...

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