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Prove that: 1/(sin(x-a)cos(x-b))=(cot(x-...

Prove that: `1/(sin(x-a)cos(x-b))=(cot(x-a)+"tan"(x-b))/(cos(a-b))`

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To prove the equation \[ \frac{1}{\sin(x-a) \cos(x-b)} = \frac{\cot(x-a) + \tan(x-b)}{\cos(a-b)}, \] we will start from the right-hand side (RHS) and manipulate it to show that it equals the left-hand side (LHS). ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi ...

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  2. If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that si...

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  3. Prove that: 1/(sin(x-a)cos(x-b))=(cot(x-a)+"tan"(x-b))/(cos(a-b))

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  4. Find the maximum and minimum values of the following expressions. (i)...

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  5. If sinA=3/5 and cosB=9/41, 0 < A < pi/2 and 0 < B < pi/2 then find the...

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  6. If cos A=4/(5), cosB=12/13 and (3pi)/2 < A, B < 2pi then find the valu...

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  7. Find the values of the following: t a n 15^0 ii. t a n 75^0

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  8. Find the values of the following: tan(13pi)/(12)

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  9. Evaluate the following: sin(7pi)/(12)cospi/4-cos(7pi)/(12)sinpi/4

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

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

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

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

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

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

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

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  19. Prove that : sin^2 6x-sin^2 4x=s in2x\ s in\ 10 x

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  20. Prove that: cos^2 2x-cos^2 6x=s in4x s in8x

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