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Show that sin(45^@+A)cos(45^@-B)+cos(45^...

Show that `sin(45^@+A)cos(45^@-B)+cos(45^@+A)cos(45^@-B)=cos(A-B)`

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A N EXCEL PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. If sinalpha=15/17 , cosbeta=12/13 and alpha and beta are in the first ...

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  2. If tanA=a/(a+1) and tanB=1/(2a+1).prove that A+B=45^@ ; ane(-1/2) and ...

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  3. Show that sin(45^@+A)cos(45^@-B)+cos(45^@+A)cos(45^@-B)=cos(A-B)

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  4. If A+B=pi/4 show that (1+tanA)(1+tanB)=2

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  5. Prove that tan70^@=tan20^@+2tan50^@

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  6. Prove that tan225^@ cot405^@+tan675^@ cot315^@=2

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  7. Prove that (sinA+sin3A+Sin5A)/(cosA+cos3A+cos5A)=tan3A

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  8. Prove that (cosA-cosB)^2+(sinA-sinB)^2=4sin^2((A-B)/2)

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  9. Prove that (sin(3A)/sinA)+(cos(3A)/cosA)=4cos2A

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  10. Prove that (tan5theta+tan3theta)/(tan5theta-tan3theta)=4cos2thetacos4t...

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  11. Prove that 1-8sin^2Acos^2A=cos4A

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  12. If 2costheta=x+(1/x) prove that 2cos3theta=x^3+(1/x^3)

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  13. If tantheta=b/a Show that acos2theta+bsin2theta=a

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  14. If tanA=1/3 and tanB=1/7 , show that 2A+B=45^@

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  15. Prove that sin^2(pi/8)+sin^2((3pi)/8)+sin^2((5pi)/8)+sin^2((7pi)/8)=2

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  16. Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

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  17. If tan(A/2)=x show that secA+tanA=(1+x)/(1-x)

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  18. Prove that sin^2(pi/6)+cos^2(pi/3)-tan^2(pi/4)=-1/2

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  19. Prove that 2sin^2(pi/6)+cosec^2((7pi)/6)cos^2(pi/3)=3/2

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  20. Prove that cot^2(pi/6)+cosec((5pi)/6)+3tan^2(pi/6)=6

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