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

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

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

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. cot A + cot (60^(@) + A) + cot (120^(@) +A) = 3 cot 3 A.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If theta = (pi)/(2 ^(n) +1) prove that 2 ^(n) cos theta cos 2 theta c...

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  18. If tan "" (x-y)/( 2 ), tan z, tan "" (x + y)/( 2) are in G.P. then sho...

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  19. If sin theta is G.M. of sin phi and cos phi, then prove that cos 2 th...

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  20. If m tan (theta - 30^(@))= n tan (theta + 120^(@)), show that cos 2 th...

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