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(sintheta)/(1+costheta)+(1+costheta)/(si...

`(sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2cosectheta`

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LHS `=frac{sin theta}{1+cos theta}+frac{1+cos theta}{sin theta} `

`Rightarrow frac{sin ^{2} theta+(1+cos theta)^{2}}{sin theta(1+cos theta)} `

`Rightarrow frac{sin ^{2} theta+1+2 cos theta+cos ^{2} theta}{sin theta(1+cos theta)} `

`Rightarrow frac{(sin ^{2} theta+cos 2 theta)+1+2 cos theta}{sin theta(1+cos theta)} [sin ^{2} theta+cos ^{2} theta=1] `

`Rightarrow frac{2+2 cos theta}{sin theta(1+cos theta)}=frac{2(1+cos theta)}{sin theta(1+cos theta)}=frac{2}{sin theta}=2 cosec theta`

= RHS
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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove the following identities: 2sec^2theta-sec^4theta-2cos e c^2th...

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  2. Prove the following identities: (sintheta-sectheta)^2+(costheta-cos e...

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  3. (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2cosectheta

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  4. Prove the following identities: (tantheta-cottheta)/(sinthetacostheta...

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  5. Prove the following identities: 1/(sectheta-tantheta)=sectheta+tanthe...

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

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  7. Prove the following identities: (tantheta+sectheta-1)/(tantheta-secth...

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

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  9. Prove the following identities: (sintheta)/(cottheta+cos e ctheta)=2+...

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  10. Prove the following identities: (cos e ctheta-sintheta)(sectheta-cost...

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  11. Prove the following identities: (1-costheta)/(1+costheta)=(cos e cthe...

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

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  13. Prove the following identities: (sin+cosA)/(sinA-cosA)+(sin-cosA)/(si...

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  14. Prove the following identities: (cos e ctheta-sintheta)(sectheta-co...

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  15. Prove that tantheta=(sintheta-2sin^3theta)/(2cos^3theta-costheta)

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  16. Prove the following identities: cot^4A-1=cos e c^4A-2cos e c^2A

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  17. Prove the following identities: sin^4A+cos^4A=1-2sin^2Acos^2A

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  18. Prove the following identities: sin^4A-cos^4A=sin^2A-cos^2A=2sin^2A-1...

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  19. Prove the following identities: sin^6A+cos^6A=1-3sin^2Acos^2A

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  20. Prove the following identities: sec^4A-sec^2A=tan^4A+tan^2A

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