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If x and y are real, show that the equat...

If x and y are real, show that the equation :
`sec^2 theta= (4xy)/(x+y)^2` is valid only when `x = y ne 0`.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that the equation : cos theta= x+1/x is impossible if x be real...

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  2. Prove that the equation : (a+b)^2= 4ab sin^2 theta is possible only w...

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  3. If x and y are real, show that the equation : sec^2 theta= (4xy)/(x+...

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  4. Find the value of the following : sin^2 30^@ + sin^2 45^@+ sin^2 60^...

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  5. Find the value of the following : (sin 60^@)/(cos^2 45^@)-3 tan 30^@...

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  6. Find the value of the following : 3 sin^2 30^@+ 2 tan^2 60^@- 5 cos^...

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  7. Find the value of the following : 2 sin^2 30^@- 3 cos^2 45^@+ cos^2 ...

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  8. Prove that : cot^2 60^@+ sin^2 45^@+ sin^2 30^@+ cos^2 90^@=13/12.

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  9. Prove that : cosec 60^@ cot 30^@ tan 60^@= 2 sec^2 45^@ cos30^@.

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  10. Prove that : cos^2 30^@, cos^2 45^@, cos^2 60^@ are in A.P.

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  11. Prove that : cot^2 30^@, cot^2 45^@, cot^2 60^@ are in G.P.

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  12. If A= 45^@, verify that : sin 2A =2 sin A cos A .

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  13. If A= 45^@, verify that : cos 2A = cos^2 A - sin^2 A.

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  14. If theta = 30^@, verify that tan 2 theta= (2 tan theta)/(1- tan^2 thet...

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  15. If A= 30^@ and B= 60^@, verify that : sin (A + B) = sin A cos B + co...

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  16. Given tan 2A = (2 tan A)/(1-tan^2A). If tan 30^@= 1/sqrt3, verify that...

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  17. Find the value of theta (0^@ le theta le 90^@) satisfying : tan theta+...

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  18. Find the value of theta (0^@ le theta le 90^@) satisfying : 2 sin^2 th...

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  19. Find the value of theta (0^@ le theta le 90^@) satisfying : 2 cos^2 th...

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  20. If sin theta= 21/29, prove that sec theta+ tan theta= 2 1/2 if theta l...

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