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Prove the following identities: 1/(cos e...

Prove the following identities: `1/(cos e cA-cotA)-1/(sinA)=1/(sinA)-1/(cos e cA+cotA)`

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Given,
`1/(cos e cA-cotA)-1/(sinA)`
`= 1/ (1/(sinA)-(cosA)/(sinA)) – 1/(sinA)`
`=1/ (1-(cosA)/(sinA))-1/(sinA)`
`=(sinA )/ (1-cosA) – 1/(sinA)` ...
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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove the following identities: (sintheta)/(1-costheta)+(tantheta)/(1...

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  2. Find (1 + tantheta + sectheta)(1+ cottheta - cosectheta)

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  3. Prove the following identities: 1/(cos e cA-cotA)-1/(sinA)=1/(sinA)-1/...

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  4. Prove the following trigonometric identities: (sintheta)/(1-costheta)=...

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  5. Prove the following trigonometric identities: sqrt((1-sintheta)/(1+sin...

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  6. Prove the following identities: (1-sintheta)/(1+sintheta)= (sectheta...

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  7. If cos e ctheta-sintheta=l and sectheta-costheta=m , prove that l^2m^2...

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  8. If tanA=ntanB and sinA=msinB, prove that cos^2A=[m^2-1]/[n^2-1]

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  9. If x=asinthetaa n dy=btantheta, then prove that (a^2)/(x^2)-(b^2)/(y^2...

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  10. If (cosalpha)/(cosbeta)=m and (cosalpha)/(sinbeta)=n show that (m^2+n^...

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  11. Prove the following identities: cos^4A-cos^2A=sin^4A-sin^2A

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  12. Prove the following identities: (sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)=1/...

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  13. If xsin^3theta+ycos^3theta=sinthetacostheta and xsintheta=ycostheta, p...

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  14. If cos e ctheta-sintheta=m and sectheta-costheta=n , prove that (m^...

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  15. Prove the following identities: (cosA)/(1-tanA)+(sin^2A)/(sinA-cosA)=...

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  16. Prove the following identities: ((1+sintheta)^2+(1-sintheta)^2)/(co...

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  17. Prove the following identities: (cos^2theta)/(1-tantheta)+(sin^3theta...

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  18. Prove the following identities: (sin^3theta+cos^3theta)/(sintheta+c...

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  19. Prove the following trigonometric identities: (tantheta+sintheta)...

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  20. Prove the following identities: (cosA)/(1-tanA)+(sinA)/(1-cotA)=cos...

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