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

` (1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x `

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. Prove that cot alpha - tan alpha =2 cot 2 alpha.

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

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  3. (1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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