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Prove that: (cos8^@-"sin"8^@)/(cos8^@+"s...

Prove that: `(cos8^@-"sin"8^@)/(cos8^@+"sin"8^@)=t a n 37^@`

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To prove that \[ \frac{\cos 8^\circ - \sin 8^\circ}{\cos 8^\circ + \sin 8^\circ} = \tan 37^\circ, \] we can follow these steps: ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. (tanA+tanB)/(tanA-tanB)=sin(A+B)/(sin(A-B)

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  2. Prove that: (cos 11^@+"sin"11^@)/(cos 11^@-"sin"11^@)=tan 56^@

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  3. Prove that: (cos8^@-"sin"8^@)/(cos8^@+"sin"8^@)=t a n 37^@

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  4. (cos9^@+sin9^@)/(cos9^@-sin9^@)= (a) tan 54^@ (b) tan 36^@ (d) None of...

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  5. Prove that: sin(60^0-theta)-cos(30^0+theta)=0.

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  6. Prove that: sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)=(sqrt...

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  7. Prove that: sin((3"pi")/8-5)cos("pi"/8+5)+cos((3"pi")/8-5)sin("pi"/8+7...

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  8. Prove that :(tan69^@+tan 66^@)/(1-tan 69^@tan66^@)=-1

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  9. If tanA=5/6 and tanB=1/(11),\ p rov e\ t h a t\ A+B=pi/4

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  10. If tanA=m/(m-1)\ and tanB=1/(2m-1), then prove that A-B=\ pi/4

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  11. Prove that: cos^2 45^@-sin^2 15^@=(sqrt(3))/4

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  12. Prove that: sin^2(n+1)A-sin^2n A="sin"(2n+1)A s in A

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  13. Prove that: (sin(A+B)+sin(A-B))/(cos(A+B)+cos(A-B))=t a n A

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  14. Prove that: (sin(A-B))/(cos A cosB)+(sin(B-C))/(cos B cos C)+(sin(C-A)...

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  15. Prove that: ("sin"(A-B))/(s in A s in B)+("sin"(B-C))/(s in B s in C)+...

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  16. Prove that: sin^2B=sin^2A+sin^2(A-B)-2sin A cos B sin(A-B)

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

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  18. Prove that: (tan(A+B))/(cot(A-B))=\ (tan^2A-tan^2B)/(1-tan^2Atan^2B)

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  19. If tan A= xtanB then prove that sin(A-B)/sin(A+B)=(x-1)/(x+1)

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  20. If tan(A+B)=x and tan(A-B)=y then find the values of tan2A and tan2B

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