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Prove: (2)/( cot alpha tan 2 alpha ) = 1...

Prove: `(2)/( cot alpha tan 2 alpha ) = 1 - tan ^(2) alpha.`

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. Prove: (sin theta xx tan ""(theta)/(2)) = 2sin ^(2) ""(theta)/( 2)

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  2. (1)/( sec 2 theta) = cos ^(4) theta - sin ^(4) theta.

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  3. Prove: (2)/( cot alpha tan 2 alpha ) = 1 - tan ^(2) alpha.

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  4. Prove that ( sin 2 A )/( 1 - cos 2 A) = cot A

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  5. Prove: ( sin 2 A)/( 1 + cos 2 A)= tan A

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  6. Prove that (sin 3 theta)/( sin theta) - (cos 3 theta)/(cos theta) = 2

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  7. Prove that (cos ^(3) A - sin ^(3) A)/( cos A - sin A ) = (2 + sin 2 A)...

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  8. Prove that (1 - cos 2 theta)/( sin 2 theta) = tan theta.

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  9. Prove that cot alpha - tan alpha =2 cot 2 alpha.

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  10. Prove that cosec A -2 cot 2 A cos A = 2 sin A.

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  11. (1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x

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  12. Show that '(1-cos 2x + sin x)/(sin 2x + cos x) = tan x'

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

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

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

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

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

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

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

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

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