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Expand cos ( A + B + C). Hence prove tha...

Expand cos ( A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C
cos A + sin C sin A cos B, if A + B + C = `(pi)/(2)`.

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The correct Answer is:
`sin A sin B cos C+ sin B sin C cos A+sin C sin A cos B`
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FULL MARKS-TRIGONOMETRY-Exercise 3.4
  1. Prove that sin (pi + theta) = - sin theta

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  2. Find a quadratic equation whose roots are sin 15^(@) and cos 15^(@)

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  3. Expand cos ( A + B + C). Hence prove that cos A cos B cos C = sin A si...

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  4. Prove that sin (45^(@) + theta) - sin (45^(@) - theta) = sqrt(2) sin...

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  5. If a cos (x + y) = b cos (x - y), show that (a + b)tan x = (a - b) cot...

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  6. Prove that sin 105^(@) + cos 105^(@) = cos 45^(@)

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  7. Prove that sin 75^(@) - sin 15^(@) = cos 105^(@) + cos 15^(@)

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  8. Show that tan 75^(@) + cot 75^(@) = 4

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

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  10. Prove that sin (n + 1)theta sin (n - 1) theta + cos (n + 1)theta cos (...

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  11. If x cos theta = y cos (theta + (2pi)/(3))= z cos (theta + (4pi)/(3)) ...

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  12. Prove that sin ( A + B) sin (A - B) = sin^(2) A - sin^(2)B.

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  13. Show that cos^(2) A + cos^(2)B - 2 cos A cos B cos (A + B) = sin^(2) (...

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  14. If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3...

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  15. Show that tan(45^(@) + A) = (1 + tan A)/(1 - tan A)

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  16. Prove that cot (A + B) = (cot A cot B - 1)/(cot A + cot B)

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  17. If tan x =(n)/(n + 1) and tan y = (1)/(2n + 1), find tan (x + y).

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  18. Prove that tan ((pi)/(4) + theta) tan ((3pi)/(4) + theta) = -1

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  19. Find the values of tan (alpha + beta), given that cot alpha = (1)/(2) ...

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  20. If theta + phi = alpha and tan theta = k tan phi, then prove that sin ...

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