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Prove that : cos^(4) A - sin^(4) A = 2...

Prove that :
`cos^(4) A - sin^(4) A = 2 cos^(2) A - 1`

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

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Prove the following identities : sin^(4) A - cos^(4) A = 2 sin^(2) A - 1

Prove that : cos 4x = 1 - 8 sin^2 x cos^2 x .

Prove that : (i) sin 60^(@) = 2 sin 30^(@) cos 30^(@) (ii) 4(sin^(4) 30^(@) + cos^(4) 60^(@)) - 3(cos^(2)45 - sin^(2)90^(@)) = 2

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ICSE-TRIGONOMETRICAL IDENTITIES-QUESTIONS
  1. Prove the identity : tan A + cot A = sec A . cosec A

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  2. Prove that : cos^(4) A - sin^(4) A = 2 cos^(2) A - 1

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  3. Prove that : (1 + cot A)^(2) + (1 - cot A)^(2) = 2 cosec^(2) A

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  4. Prove that : tan^(4) A + tan^(2) A = sec^(4) A - sec^(2) A

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

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  6. Prove that : (1 + cos A)/(1 - cos A) = (cosec A + cot A)^(2)

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  7. Prove that : (cot A + tan B)/ (cot B + tan A) = cot A tan B

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  8. Prove that : (cos A cot A)/ (1 - sin A) = 1 + cosec A

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  9. Prove that : (sec A - tan A)/ (cosec A + cot A) = (cosec A - cot A)/...

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  10. Prove that : sqrt ((1 - sin A)/(1 + sin A)) = sec A - tan A

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  11. Prove that : (tan A + sec A - 1)/ (tan A - sec A + 1) = (1 + sin A)/...

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  12. Prove that : (cos A)/ (1 - tan A) + (sin A)/ (1 - cot A) = cos A + s...

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  13. Prove that : (1 + tan^(2) A) + (1 + (1)/ (tan^(2) A)) = (1)/ (sin^(2...

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  14. If tan A + sin A = m and tan A - sin A = n, prove that : m^(2) -...

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  15. If x = a sec A cos B, y = b sec A sin B and z = c tan A, show that...

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  16. Find the value of x, if : cos x = cos 60^(@) cos 30^(@) + sin 60^(@)...

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  17. Given: cos 38^(@)sec(90^(@)-2A)=1, find the value of angle A.

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  18. Find : sin 36^(@) 51'

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  19. Find : tan 53^(@) 38'

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  20. Find : cos 62^(@) 27'

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