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Prove the following identities: (sinthe...

Prove the following identities: `(sintheta+cos e ctheta)^2+(costheta+sectheta)^2=7+tan^2theta+cot^2theta`

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Given,
`(sintheta+cosectheta)^2+(costheta+sectheta)^2`
`=sin^2theta+cosec^2theta+2sintheta.cosectheta+cos^2theta+sec^2theta+2costheta.sectheta`
`=(sin^2theta+cos^2theta)+1+cot^2theta+2+1+tan^2theta+2`
`=1+6+tan^2theta+cot^2theta` ...
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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(...

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

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  3. Prove the following identities: (sintheta+cos e ctheta)^2+(costheta+s...

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  4. Prove the following identities: (sintheta)/(1-costheta)+(tantheta)/(1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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