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If x = rsin theta*cos phi, y = rsin thet...

If `x = rsin theta*cos phi`, `y = rsin theta*sin phi` and `z = rcos theta` then prove that `x^2 + y^2 + z^2 = r^2`

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. The maximum value of 5cos theta + 12 sin theta is 17. Given statement ...

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  2. If cos x + cos y- cos(x +y) = 3/2 then x=y is possible.

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  3. If x = rsin theta*cos phi, y = rsin theta*sin phi and z = rcos theta ...

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  4. The minimum value of 3cos x + 4sin x + 5 is 0. Given statement is true...

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  5. tan 22 1^circ/2 is a root of the equation - (1+x^(2))/(1- x^(2)) = sq...

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  6. If tan theta= 2 is satisfied by alpha, beta then the value of frac{tan...

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  7. Prove that sin 1^circ lt sin 1.

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  8. If sin alpha = -3/5,pi lt alpha lt 3pi/2 then cos alpha/2 = 1/sqrt10

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  9. In the following incomplete sentences fill in the blanks such that the...

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  10. If sin 17^circ *sin 43^circ *sin 77^circ = lambda sin 51^circ then lam...

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  11. In the following incomplete sentences fill in the blanks such that the...

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  12. In the following incomplete sentences fill in the blanks such that the...

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  13. In the following incomplete sentences fill in the blanks such that the...

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  14. If un = 2cos n theta then u1un - u(n-1) is equal to

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  15. If frac {x}{cos theta} = frac {y}{cos(theta -(2pi)/3)} = frac {z}{co...

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  16. If cos alpha + cos beta + cos gamma = 0 then cos 3alpha + cos 3beta + ...

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  17. tan 40^circ + 2tan 10^circ is equal to

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  18. A factor of cos 4theta - cos 4phi is

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  19. The chord AB of a circle subtends an angle of frac {2pi}{3} at a point...

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  20. If sin alpha + cos alpha = lambda then find |sin^(6) alpha - cos^(6) a...

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