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Prove the following identities: (1+tanAt...

Prove the following identities: `(1+tanAtanB)^2+(tan"A"-tan"B")^2=sec^2Asec^2B` `(tan"A"+"c o s e cB")^2-(cot"B"-sec"A")^2=2tanAcotB(cos e cA+secB)`

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`(i)(1+tanAtanB)^2+(tan"A"-tan"B")^2=sec^2Asec^2B`
`=tan^2A+tan^2B−2tanAtanB+1+tan^2Atan^2B+2tanAtanB`
`=tan^2A+tan^2B+1+tan^2(A)tan^2(B)`
`=tan^2(A)[1+tan^2(B)]+[1+tan^2(B)]`
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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove that (1-sintheta+costheta)^2=2(1+costheta)(1-sintheta)

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  2. Prove the following identities: (sinA+secA)^2+(cos"A"+"c o s e cA")^2=...

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  3. Prove the following identities: (1+tanAtanB)^2+(tan"A"-tan"B")^2=sec^2...

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  4. Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+...

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  5. Prove the following identities: tan^2A-tan^2B=(cos^2B-cos^2A)/(cos^2Bc...

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  6. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

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  7. If tantheta+sintheta=m and tantheta-sintheta=n , then m^2-n^2=

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  8. if (secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB) (secC-t...

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  9. Prove the following identities: (cosA)/(1-sinA)+(sinA)/(1-cosA)+1 = (...

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  10. If tan^2theta=1-a^2, prove thats e ctheta+tan^3thetacos e ctheta=(2-a^...

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  11. If a sectheta+bt a ntheta+c=0 and psectheta+qtantheta+r=0, prove that...

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  12. If sectheta+tantheta=p , show that (p^2-1)/(p^2+1)=sintheta

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  13. If sintheta+costheta=pa n dsectheta+cos e ctheta=q , show that q(p^2-1...

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  14. Without using trigonometric tables, evaluate each of the following: (...

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  15. Without using trigonometric tables, evaluate each of the following: (...

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  16. Prove the trigonometric identities: (1-sintheta)/(1+sintheta)=(secthe...

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  17. Prove the trigonometric identities: sqrt((1-costheta)/(1+costheta))=co...

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  18. If sectheta=x+1/(4x) ,prove that :sectheta+tantheta=2xor ,1/(2x)

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  19. Prove that : (sinthetacos(90^0-theta)costheta)/(sin(90^0-theta))+(cost...

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  20. If sectheta+tantheta=x , obtain the values of sectheta,t a ntheta and...

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