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If A-B=pi/4, then prove that: (1+tanA)...

If `A-B=pi/4`, then prove that:
`(1+tanA)(1-tanB)=2`

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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. Prove that: i) tan36^(@)+tan9^(@)+tan36^(@)tan9^(@)=1

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  2. Prove that: (cos8^(@)-sin8^(@))/(cos8^(@)+sin8^(@))=cot53^(@)

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  3. If A-B=pi/4, then prove that: (1+tanA)(1-tanB)=2

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  4. Prove that: (cos(60^(@)-A)+sin(30^(@)-A))/(cos(30^(@)-A)-sin(60^(@)-A)...

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  5. i) If A+B=pi/4 prove that: (cotA-1)(cotB-1)=2

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  6. Prove that: (tan(pi/4+A)+tan(pi/4-A))/(tan(pi/4+A)-tan(pi/4-A))="cos...

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  7. Prove that: (sin(A-B))/(cosAcosB)+(sin(B-C))/(cosBcosc)+(sin(C-A))/(...

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  8. Prove that: sinAsin(B-C)+sinBsin(C-A)+sinCsin(A-B)=0

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  9. Prove that: cot2Acot3A-cot3Acot5A-cot5Acot2A=1

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  10. Prove that: cotA-cot2A="cosec"2A

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  11. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

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  12. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  13. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  14. If 2tanB +cotB=tanA, prove that: 2tan(A-B)=cotB

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  15. i) If tan (A+B) = n tan (A-B), prove that: (n+1)/(n-1) = (sin2A)/(sin...

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  16. If A+B=225^(@), then find the value of (cotA)/(1+cotA)xx(cot B)/(1+cot...

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  17. If cos(A+B)sin(C-D)="cos"(A-B)"sin"(C+D) , then write the value of t a...

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  18. If alphaa n dbeta are the solutions of acostheta+bs intheta=c , then s...

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  19. If sinA + sinB = a and cosA+cosB=b, prove that: i) sin(A+B)=(2ab)/(a...

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  20. Prove that the value of 5 costheta+3 cos(theta+pi/3) lies between -7 a...

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