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

Prove that `((cos A + cos B)/( sin A - sin B )) ^(n) + ((sin A + sin B )/( cos A - cos B )) ^(n) ={{:(2 cot ^(n) ((A- B)/(2)),"," "if n is even."),(0,",""if n is odd."):}.`

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ICSE-COMPOUND AND MULTIPLE ANGLES -CHEPTER TEST
  1. Show that (sin (alpha + beta))/( sin (alpha + beta)) = 2, given that ...

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  2. Show that ( cos 10^(@) + sin 10 ^(@))/( cos 10^(@) - sin 10 ^(@)) = ta...

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  3. If sin 2 A = 4/5, find the value of tan A, (0^(@) le A le (pi)/(3))

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  4. Express cot A in terms of cos 2 A

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  5. Write cos 4 theta in terms of cos theta.

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  6. A positive acute angle is divided into two parts whose tangents are 1/...

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  7. Show that cos 10^(@) + cos 110^(@) + cos 130^(@) = 0

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  8. Show that (sin 5 A + 2 sin 8A + sin 11 A)/( sin 8A + 2 sin 11 A + sin ...

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  9. Show that (1)/(2 sin 10^(@)) - 2 sin 70^(@) =1.

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  10. Show that sin 19^(@) + sin 41^(@) + sin 83^(@) = sin 23 ^(@) + sin 37^...

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  11. If sin A = (1)/(sqrt3) and sin B = (1)/(sqrt5) find the value of tan...

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  12. If sin theta = n sin ( theta + 2 alpha ) , show that ( n -1) tan (the...

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  13. If tan "" (alpha )/(2) and tan "" (beta)/( 2) are the roots of the eq...

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  14. Prove that ((cos A + cos B)/( sin A - sin B )) ^(n) + ((sin A + sin B ...

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  15. Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the c...

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  16. Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the c...

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  17. Prove that cos 6x = 32 cos ^(6) x - 48 cos ^(4) x + 18 cos ^(2) x -1.

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  18. Prove that sin ^(2) 72 ^(@)- sin ^(2) 60 ^(@)= (sqrt5-1)/(8).

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  19. If tan x, tan y, tan z are in G.P., show that cos 2y = (cos (x +z))/(...

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  20. If tan (alpha )/(2) : tan ""(beta)/(2) = 1 : sqrt3 show that cos beta...

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