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Prove that: cos(pi/4-A)cos(pi/4-B)-sin(p...

Prove that: `cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)="sin"(A+B)`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-All Questions
  1. Evaluate the following: sin(7pi)/(12)cospi/4-cos(7pi)/(12)sinpi/4

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  2. Evaluate the following: cos(2pi/3)cos(pi/4)-sin(2pi/3)sin(pi/4)

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  3. Prove that: cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)="sin"(A+B)

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  4. Prove that: sin(n+1)A sin(n+2)A+cos(n+1)A cos(n+2)A=cos A

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  5. Prove that: cos(pi/4+x)+cos(pi/4-x\ )=sqrt(2)cosx

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  6. Prove that: cos((3pi)/4+x)-cos((3pi)/4-x\ )=sqrt(2)sinx

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  7. Prove that: sin(x+y)/sin(x-y)=(tanx+tany)/(tanx-tany)

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  8. Prove that (tan(pi/4+x))/(tan(pi/4-x))=((1+t a n x)/(1-t a n x))^2

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  9. if tanalpha=1/(sqrt(x(x^2+x+1))), tanbeta=(sqrtx)/(sqrt(x^2+x+1) and ...

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  10. Prove that :(tan(A+B))/("cot"(A-B))=(sin^2A-sin^2B)/(cos^2A-sin^2B)

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  11. Prove that : sin^2 6x-sin^2 4x=sin 2x\ sin\ 10 x

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  12. Prove that: cos^2 2x-cos^2 6x= sin4x sin8x

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  13. Prove that: (cos^2 33^@-cos^2 57^@)/(sin^2(21/2)^@-sin^2(69/2)^@)=-sqr...

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  14. Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=co...

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  15. Prove that: t a n 70^0=t a n 20^0+2t a n 50^0dot

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  16. If sin alpha+sin beta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  17. If sin alpha+sin beta=a\ a n d\ cosalpha+cosbeta=b , show that : sin(a...

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  18. If sinA=4/5 and cosB=5/13, find the value of the following : "sin"(A+B...

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  19. If sinA=4/5 and cosB=5/(13), where 0 < A,B < pi/2 ,find the value of...

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  20. If sinA=4/5 and cosB=5/(13),where 0ltAltpi/2 ;0ltBltpi/2 , find the ...

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