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If sintheta+costheta=x, then show that: ...

If `sintheta+costheta=x`, then show that:
`sin^(6)theta+cos^(6)theta=1-3/4(x^(2)-1)^(2)`

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NAGEEN PRAKASHAN-TRIGNOMETRIC FUNCTIONS-EXERCISES 3B
  1. Prove that: (1-tanA)^(2)+(1-cotA)^(2)=(secA-"cosec"A)^(2)

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  2. i) Prove that: (1+tan^(2)A)/(1-tan^(2)A) xx (2 cos^(2) A-1)=1 ii) Pr...

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  3. Prove that: sinA(1+tanA)+cosA(1+cotA)= secA+"cosec"A

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  4. Prove that: (1+cosA+sinA)/(1+cosA-sinA)=(1+sinA)/(cosA)

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  5. Prove that: 2sec^(2)A-sec^(4)A-2"cosec"^(2)A+"cosec"^(4)A=cot^(4)A-t...

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  6. Prove that: 1-(sin^(2)A)/(1+cotA)-(cos^(2)A)/(1+tanA)=sinA.cosA

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  7. i) Prove that: (cot^(2)A)/(1-"cosec"A)^(2)=(1+sinA)/(1-sinA) ii) Pro...

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  8. Prove that: (secAsecB+tanAtanB)^(2)-(secAtanB+tanAsecB)^(2)=1

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  9. Prove that: 3(sinA-cosA)^(4)+6(sinA+cosA)^(2)+4(sin^(6)A+cos^(6)A)=13

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  10. i) Prove that: [(1-sinA)/(1-secA)-(1+sinA)/(1+secA)]=2cotA(cosA-"cose...

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  11. If costheta-sintheta=sqrt(2)sintheta, then prove that: costheta+sint...

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  12. If asin^(2)theta+bcos^(2)theta=c, then prove that tan^(2)theta=(c-b)/(...

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  13. i) If acostheta+bsintheta=m and asintheta-bcostheta=n, then prove that...

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  14. If acostheta-bsintheta=c, then prove that: asintheta+bcostheta=+-sqr...

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  15. If cottheta(1+sintheta)=4m and cottheta(1-sintheta)=4n, then prove tha...

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  16. If tantheta+sintheta=m and tantheta-sintheta=n, then prove that: m^(2)...

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  17. If acostheta+bsintheta=c, then prove that: asintheta-bcostheta=+-sqr...

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  18. If (1-sinA)(1-sinB)(1-sinC)=(1+sinA)(1+sinB)(1+sinC), then prove that ...

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  19. If tan^(2)theta=1-m^(2), then show that: sectheta+tan^(3)theta."cose...

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  20. If sintheta+costheta=x, then show that: sin^(6)theta+cos^(6)theta=1-...

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