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If cos A=5/13 and sin B= 4/5 , find sin...

If `cos A=5/13` and `sin B= 4/5` ,
find sin (A + B), where A, B, (A + B) are positive acute angles.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : tan 50^@ = tan 40^@ + 2 tan 10^@ .

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

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

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

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

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

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

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

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  9. Prove that : (cos^2 33^@- cos^2 57^@)/(sin^2 frac (21^@) (2)- sin^2 fr...

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  10. Find a and b such that a le3 cos theta +5 sin (theta-pi/6)le b holds ...

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  11. If sin alpha=15/17 and cos beta=12/13, find the values of : sin (alpha...

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  12. If sin alpha=15/17 and cos beta=12/13, find the values of : cos (alph...

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  13. If sin alpha=15/17 and cos beta=12/13, find the values of : tan (alph...

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  14. If cos (alpha+beta)=4/5, sin (alpha -beta)=5/13 and alpha, beta lie b...

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  15. Find the value of tan (alpha+beta), given that : cot alpha=1/2, alpha...

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  16. If theta+phi= alpha and tan theta=k tan phi, prove that : sin alpha=(...

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  17. Prove the following: cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt2 sinx

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  18. Prove that cos((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt(2)cosx

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  19. Prove the following : (sin 5x + sin3x)/(cos 5x + cos 3x)= tan 4x.

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  20. Prove the following : (sinx +siny)/(cos x+cos y)= tan frac (x+y)(2).

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