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

If `theta = (pi)/(2 ^(n) +1) ` prove that `2 ^(n) cos theta cos 2 theta cos 2 ^(2) theta…. Cos 2 ^(n -1) theta =1 `

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. cos ^(2) 36^(@) + sin ^(2) 18^(@) = (3)/(4).

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  2. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If sin alpha = lamda sin (theta - alpha ) then prove that tan (alpha...

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  20. If tan ""(alpha )/(2) = sqrt ({(1 -e)/( 1 +e)}) tan ""(beta)/(2), Prov...

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