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tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 7...

`tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1`

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Show that tan48^(@) tan 23^(@) tan 42^(@) tan 67^(@) =1 .

Show that : (i) tan 10^(@) tan 15^(@) tan 75^(@) tan 80^(@) = 1 (ii) sin 42^(@) sec 48^(@) + cos 42^(@) "cosec 48"^(@) = 2

If tan 69^(@) + tan 66^(@) - tan 69^(@)tan 66^(@) = 2k then k = (a) -(1)/(2) (b) (1)/(2) (c) -1 (d)None of these

tan 75 ^(@) - tan 30^(@)- tan 75^(@) tan 30^(@) =1.

Show that: tan 10^(@)tan 15^(@) tan 75^(@)tan 80^(@)=1

Prove that: tan10^(@) tan20^(@)tan70^(@)tan80^(@)=1

Shown that : tan48^(@)tan23^(@)tan42^(@)tan67^(@)=1

(tan8 0^(@)-tan1 0^(@))/tan70^(@)

Simplify be reducing to a single term : (tan 69^(@) + tan 66^(@))/(1 - tan 69^(@) tan 66 ^(@))

Prove that tan 12^@ tan 24^@ tan 48^@ tan 84^@ = 1 .

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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