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Prove that 4(cos ^(3) 10^(@) + sin ^(3) ...

Prove that `4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin 20^(@)).`

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i) Prove that: cos^(3)2A+3cos2A = 4(cos^(6)A-sin^(6)A) ii) Prove that: 4(cos^(3)10^(@) + sin^(3)20^(@)) = 3(cos10^(@)+sin20^(@))

4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

What is the value of (cos 10 ^(@) + sin 20^(@))/( cos 20^(@) - sin 10 ^(@))?

Prove that (cos ^(3) A - sin ^(3) A)/( cos A - sin A ) = (2 + sin 2 A)/( 2 ).

Prove that sin 20^(@) sin 40^(@) sin 80^(@) = (sqrt3)/(8).

Prove that : 4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)90^(@))=2

Prove that : 4(sin^(4)30^(@)+cos^(4)60^(@))-3(cos^(2)45^(@)-sin^(2)90^(@))=2

Prove that : (cos^(3) A + sin^(3) A)/ (cos A + sin A) + (cos^(3) A - sin^(3) A)/(cos A - sin A) = 2

(1)/(sin 10^(@)) - (sqrt3)/(cos 10 ^(@)) = 4.

Prove that : (i) sin42^(@)cos48^(@)+sin48^(@)cos42^(@)=1 (ii) cos70^(@)cos20^(@)-sin70^(@)sin20^(@)=0

ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 cot 8 theta = cot theta.

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  2. 4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

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  3. Prove that 4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin...

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  4. Prove that cos ^(3) x sin ^(2) x = (1)/(16) (2cos x - cos 3x - cos 5x)...

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  5. cot A + cot (60^(@) + A) + cot (120^(@) +A) = 3 cot 3 A.

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  6. Prove that : cos 36 ^(@) - sin 18^(@) = (1)/(2).

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  7. cos ^(2) 36^(@) + sin ^(2) 18^(@) = (3)/(4).

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  8. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

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  9. cos ^(2) 48^(@) - sin ^(2) 12 ^(@) = (sqrt5+1)/(8).

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  10. Prove that sin "" (1)/(10) pi cos ""(1)/(5) pi = (1)/(4).

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  11. sec 72 ^(@) - sec 36^(@) = 2.

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  12. sin ^(2) 24 ^(@) - sin ^(2) 6^(@) = (sqrt5 -1)/(8).

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  13. sin 12 ^(@) sin 48^(@) sin 54 ^(@) = (1)/(8).

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  14. Prove that 4 cos 6^(@) cos 42 ^(@) cos 66^(@) cos 78^(@) = (1)/(4).

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  15. sin "" (pi)/(5) sin "" (2pi)/(5) sin ""(4pi)/(5) sin""(3pi)/(5) = (5)/...

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  16. Prove that cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "...

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  17. cos ^(2) ""(pi)/(10) + cos ^(2) ""(2pi)/(5) + cos^(2) ""(3pi)/(5) + co...

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  18. tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1

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  19. cos alpha cos 2 alpha cos 4 alpha cos 8 alpha = (1)/(16), if alpha =...

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  20. cos 12 ^(@) cos 24 ^(@) cos 36 ^(@) cos 48^(@) cos 72^(@) cos 84^(@) =...

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