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If x=rsinthetacosphi,y=rsinthetasinphi ...

If `x=rsinthetacosphi,y=rsinthetasinphi and z=rcostheta, then x^2+y^2+z^2` is independent of `theta,phi` (b) `r ,theta` (c) `r ,phi` (d) r

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To solve the problem, we need to calculate \( x^2 + y^2 + z^2 \) given the expressions for \( x \), \( y \), and \( z \). 1. **Given Expressions:** \[ x = r \sin \theta \cos \phi \] \[ y = r \sin \theta \sin \phi ...
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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
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  2. If (3pi)/4ltalphaltpi, t h e nsqrt(2cotalpha+1/(sin^2alpha)) is equal ...

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  3. If x=rsinthetacosphi,y=rsinthetasinphi and z=rcostheta, then x^2+y^2+...

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  4. If sintheta+costheta=0 and theta lies in the fourth quadrant, find si...

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  5. Prove that: sqrt((1-sintheta)/(1+sintheta))+sqrt((1+sintheta)/(1-sinth...

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  6. Prove that: cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1

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  7. Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x) = cot^2x

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  8. If x=(2sintheta)/(1+costheta+sintheta) , then prove that (1-costheta+...

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  9. If tanx=(b)/(a), then find the value of sqrt((a+b)/( a-b ))+sqrt((a-b)...

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  10. Find the values of the following trigonometric ratios. (i)cosec390^0 ...

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  11. Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.

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  12. Prove that: "sec"((3pi)/2-theta)"sec"(theta-(5pi)/2)+t a n((5pi)/2+the...

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  13. Find the value of : sin^2(pi/(18))+sin^2(pi/9)+sin^2((7pi)/(18))+sin^2...

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  14. If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A...

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  15. Find the value of the expression 3{sin^4((3pi)/2-theta)+sin^4(3pi+the...

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  16. If t a n^2theta=1-a^2 , prove that sectheta+t a n^3thetacos e ctheta=...

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  17. If acos^2theta+3acostheta sin^2theta=m and asin^3theta+3acos^2thetasin...

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  18. If 2t a n^2alphat a n^2betat a n^2gamma+t a n^2alphat a n^2beta+t a ...

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  19. If m^2 + m'^2 + 2mm' costheta = 1 and n^2+n'^2+2n n'costheta=1, (mn +...

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  20. If (sin^4theta)/a+(cos^4theta)/b=1/(a+b) , prove that (sin^8theta)/...

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