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Prove that : cos 105^@ + cos 15^@= sin 7...

Prove that : `cos 105^@ + cos 15^@= sin 75^@- sin 15^@` .

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Prove that : sin 105^@ + cos 105^@ = cos 45^@ .

Prove that : cos 130^@ cos 40^@+ sin 130^@ sin 40^@= 0 .

Prove that : sin 105^@ + cos 105^@=1/sqrt2 .

Prove that: cos15^@-sin15^@=1/sqrt2

Prove that cot 7 1^@/2 = (1+cos15^@)/(sin 15^@) .

Prove that: sin 150^@ cos 120^@+ cos 330^@ sin 660^@= - 1 .

Prove that : sin70^@ cos 10^@- cos70^@ sin 10^@= sqrt3/2 .

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Prove that : cos (A + B) = cos A cos B - sin A sin B .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Evaluate : sin 75^@, cos 75^@, tan 75^@.

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  2. Prove that : sin 105^@ + cos 105^@=1/sqrt2.

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  3. Prove that : cos 105^@ + cos 15^@= sin 75^@- sin 15^@ .

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  4. Find tan 15^@ and hence show that tan 15^@+ cot 15^@ = 4.

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  5. Evaluate : sin^2 (15^@ + A) - sin^2 (15^@ -A).

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  6. Write down the values of : cos 68^@ cos 8^@ + sin 68^@ sin 8^@.

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  7. Write down the values of : cos 70^@ cos 10^@ + sin 70^@ sin 10^@.

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  8. Prove that : cos 130^@ cos 40^@+ sin 130^@ sin 40^@= 0.

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  9. Prove that : sin (40^@+theta)cos (10^@+theta)-cos (40^@+theta) sin (10...

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  10. Prove the following: sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n +...

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  11. Prove that (sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)

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  12. Prove that (sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)

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  13. Evaluate : tan frac (13 pi)(12).

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  14. Find the maximum and minimum values of : 15 cos theta-8 sin theta.

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  15. Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B)...

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  16. If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that ...

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  17. If theta+phi=45^@, prove that (cot theta-1) (cot phi-1) =2.

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

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

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

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