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If sin A = (3)/(5) and cos B = (9)/(41),...

If sin A = `(3)/(5)` and cos B = `(9)/(41)`, 0 `lt A lt (pi)/(2), 0 lt B lt (pi)/(2)`
Find the value of
sin (A + B)

Text Solution

Verified by Experts

The correct Answer is:
(i) `(187)/(205)` (ii) `(156)/(205)`
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FULL MARKS-TRIGONOMETRY-Exercise 3.4
  1. If sin x = (15)/(17) and cos y = (12)/(13),0 lt x lt (pi)/(2) , 0 lt y...

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  2. If sin A = (3)/(5) and cos B = (9)/(41), 0 lt A lt (pi)/(2), 0 lt B lt...

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  3. Find cos (x - y), given that cos x = -(4)/(5) with pi lt x lt (3pi)/(2...

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  4. Find sin (x - y) given that sin x = (8)/(17) with 0lt x lt (pi)/(2) an...

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  5. Find the value of cos 105^(@)

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  6. Prove that sin (pi + theta) = - sin theta

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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