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If A=30^(@), then prove that : cos2A=c...

If `A=30^(@)`, then prove that :
`cos2A=cos^(2)A-sin^(2)A`
`" "=(1-tan^(2)A)/(1+tan^(2)A)`

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ICSE-TRIGONOMETRICAL RATIOS OF STANDARD ANGLES-EXERCISE 23(B)
  1. If A=30^(@), show that : (1+sin2A+cos2A)/(sinA+cosA)=2cosA.

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  2. If A=30^(@), show that : 4cosAcos(60^(@)-A)*cos(60^(@)+A)=cos3A

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  3. If A=30^(@), show that : (cos^(3)A-cos3A)/(cosA)+(sin^(3)A+sin3A)/(s...

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  4. Given A=60^(@) and B=30^(@), prove that : sin(A+B)=sinAcosB+cosAsinB

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  5. Given A=60^(@) and B=30^(@), prove that : cos(A+B)=cosAcosB-sinAsinB

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  6. Given A=60^(@) and B=30^(@), prove that : cos(A-B)=cosAcosB+sinAsinB

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  7. Given A=60^(@) and B=30^(@), prove that : tan(A-B)=(tanA-tanB)/(1+ta...

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  8. If A=30^(@), then prove that : sin2A=2sinAcosA=(2tanA)/(1+tan^(2)A)

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  9. If A=30^(@), then prove that : cos2A=cos^(2)A-sin^(2)A " "=(...

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  10. If A=30^(@), then prove that : 2cos^(2)A-1=1-2sin^(2)A

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  11. If A=30^(@), then prove that : sin3A=3sinA-4sin^(3)A

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  12. If A=B=45^(@), show that : sin(A-B)=sinAcosB-cosAsinB

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  13. If A=B=45^(@), show that : cos(A+B)=cosAcosB-sinAsinB

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  14. If A=30^(@), show that : sin3A=4sinAsin(60^(@)-A)sin(60^(@)+A)

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  15. If A=30^(@), show that : (sinA-cosA)^(2)=1-sin2A

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  16. If A=30^(@), show that : cos2A=cos^(4)A-sin^(4)A

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  17. If A=30^(@), show that : (1-cos2A)/(sin2A)=tanA

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  18. If A=30^(@), show that : (1+sin2A+cos2A)/(sinA+cosA)=2cosA.

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  19. If A=30^(@), show that : 4cosAcos(60^(@)-A)*cos(60^(@)+A)=cos3A

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  20. If A=30^(@), show that : (cos^(3)A-cos3A)/(cosA)+(sin^(3)A+sin3A)/(s...

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