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Prove the following identities: tan...

Prove the following identities: `tan^2theta+cot^2theta+2=sec^2thetacos e c^2theta`

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We have,
LHS=`tan^2 theta+cot^2 theta+2=(1+tan^2 theta)+(1+cot^2theta)`
`sec^2 theta+cosec^2 theta=1/cos^2 theta+1/sin^2 theta=(sin^2theta+cos^2theta)/(cos^2 thetasin^2theta)`
`1/(cos^2 theta sin^2 theta)=cosec^2 thetasec^2 theta`=RHS
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tan^(2)theta+cot^(2)theta+2=sec^(2)theta cosec^(2)theta

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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove the following trigonometric identities: cottheta-tantheta=(2cos...

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  2. Prove the following trigonometric identities: tantheta-cottheta=(2sin...

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  3. Prove the following identities: tan^2theta+cot^2theta+2=sec^2thet...

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  4. Prove the following identities: sqrt(sec^2theta+cos e c^2theta)=t...

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

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  6. Prove the following identities: (cos e ctheta-cottheta)^2=(1-costheta...

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

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  8. Prove the following identities: 2sec^2theta-sec^4theta-2cos e c^2th...

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

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

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

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

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

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

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

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

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

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

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

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

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