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If theta - phi=pi/4, prove that : (1 +...

If `theta - phi=pi/4`, prove that :
`(1 + tan theta)(1+tan phi)=2 tan theta`.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If theta+phi=45^@, prove that (cot theta-1) (cot phi-1) =2.

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  2. If theta - phi=pi/4, prove that : (1 + tan theta)(1-tan phi)=2.

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  3. If theta - phi=pi/4, prove that : (1 + tan theta)(1+tan phi)=2 tan ...

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  4. Prove that : tan 69^@ + tan 66^@+ 1 = tan 69^@ tan 66^@.

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  5. Prove that : (cos13^@+sin13^@)/(cos13^@-sin13^@) =tan 58^@.

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  6. Prove the following: cot x cot 2x -cot 2x cot 3x -cot 3x cot x = 1

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  7. Prove that : tan 3A - tan 2A - tan A = tan 3A tan 2A tan A.

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  8. Prove that : tan 7A -tan 5A-tan 2 A = tan 7A tan 5A tan 2A.

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  9. Prove that : tan 13A-tan 9A- tan 4A= tan 13A tan 9A tan 4A.

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  10. If cos (alpha+beta) sin (gamma+delta)=cos (alpha-beta) sin (gamma-delt...

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  11. Prove that : 1+tan A tan frac (A)(2)= secA= tanA cot frac (A)(2)-1

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  12. If cot alpha cot beta=2, show that (cos (alpha+beta))/(cos (alpha-beta...

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  13. Prove that : tan 50^@ = tan 40^@ + 2 tan 10^@ .

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  14. Prove that : 2 tan 70^@ = tan 80^@ - tan 10^@.

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  15. If cos A=5/13 and sin B= 4/5 , find sin (A + B), where A, B, (A + B) ...

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  16. If tan x= a/(a+1) and tan y=1/(2a+1), show that one of the values of :...

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  17. In any quadrilateral ABCD, show that : cos A cos B - cos C cos D = si...

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  18. Prove that : cos theta- sin theta= sqrt2 cos (theta+ pi/4).

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  19. Prove that : tan (x-y)+tan (y -z) + tan (z-x)= tan (x-y)tan (y -z) t...

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  20. Prove that : cos^2 (pi/8+x/2)-sin^2 (pi/8-x/2)= 1/sqrt2 cos x.

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