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cot A =1/2 (cot ""(A)/(2) - tan "" (A)/(...

`cot A =1/2 (cot ""(A)/(2) - tan "" (A)/(2)).`

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. Show that '(1-cos 2x + sin x)/(sin 2x + cos x) = tan x'

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  2. (sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

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  3. cot A =1/2 (cot ""(A)/(2) - tan "" (A)/(2)).

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  4. (cos A + sin A )/( cos A - sin A) - (cos A - sin A )/(cos A + sin A )...

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  5. (cos A - sin A )/( cos A + sin A ) = sec 2 A - tan 2 A.

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  6. Prove that (sin 2 A )/(1- cos 2 A ) . (1- cos A )/( cos A ) = tan ""(A...

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  7. Prove that : 2 cos A = sqrt ([2 + sqrt (2 (1 + cos 4 A))]) , A in I or...

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  8. tan 2 A = (sec 2 A +1 ) sqrt ( (sec ^(2) A -1)) , A belongs to I or IV...

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  9. Prove that (sec 8A-1)/( sec 4 A -1) = ( tan 8 A)/( tan 2A).

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  10. Prove that tan 2 A - sec A sin A = tan A sec 2 A.

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  11. Prove that (cos A + cos B ) ^(2) +(sin A + sin B) ^(2) = 4 cos ^(2) ((...

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  12. Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) (...

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  13. Prove that: cos ^(4) ""(pi)/(8) + cos ^(4) ""(3pi)/(8) + sin ^(4) "" (...

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  14. sin ^(4) "" (pi)/(8) + sin ^(4) "" (3pi)/(8) + sin ^(4) "" (5pi)/(8) +...

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  15. cos alpha cos(60^(@) - alpha ) cos (60^(@) + alpha ) = 1/4 cos 3 alpha...

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  16. (cos ^(3) alpha - cos 3 alpha )/( cos alpha ) + (sin ^(3)alpha + sin 3...

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  17. cos ^(2) 2 theta - sin ^(2) theta = cos theta . cos 3 theta.

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  18. 1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin t...

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  19. Prove that cos ^(3) (x-(2pi)/(3)) + cos ^(3) x + cos ^(3) (x + (2pi)/(...

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

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