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Prove that : cos theta- sin theta= sqr...

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

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If tan x= a/(a+1) and tan y=1/(2a+1), show that one of the values of :...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Prove the following : (sinx +sin3x)/(cos x + cos 3x)= tan 2x.

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  19. Prove the following: (sin x-sin y)/(cosx + cos y)=tanfrac(x-y)(2)

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  20. Prove the following : (cos 7x + cos 5x)/(sin 7x-sin 5x) =cot x.

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