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Prove that `sqrt ( 2 + sqrt (2 + sqrt (2 + 2 cos 8 theta))) = 2 cos theta,` where ` theta in [ (-pi)/(8), (pi)/(8)]`

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ICSE-COMPOUND AND MULTIPLE ANGLES -CHEPTER TEST
  1. Prove that sqrt ( 2 + sqrt (2 + sqrt (2 + 2 cos 8 theta))) = 2 cos the...

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  2. Show that tan 75^(@) = (sqrt3) +(1 )/( sqrt3 -1) = 2 + sqrt3. Hence de...

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  3. Prove that sin (n+1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos ...

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  4. if A+ B + C = pi, and cos A = cos B cos C, show that 2 cot B cot C=1.

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  5. Show that (sin (alpha + beta))/( sin (alpha + beta)) = 2, given that ...

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

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

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  8. Express cot A in terms of cos 2 A

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

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

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

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

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

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

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

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

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

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

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

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

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

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