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Prove the following: tan[pi/4+1/2cos^(...

Prove the following: `tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)(a/b)]=(2b)/a`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Evaluate: cos{sin^(-1)(-7/(25))} (ii) sec{cot^(-1)(-5/(12))} cot{se...

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  2. Prove that: sin^(-1)(3/5)=tan^(-1)(3/4)

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  3. Prove the following: tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)...

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  4. If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha...

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  5. if, sin^-1x + sin^-1y + sin^-1z =pi then prove that xsqrt(1-x^2) + ys...

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  6. If x = cosec[tan^(-1){"cos"(cot^(-1)(sec(sin^(-1)a)))}] and y="sec"[c...

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  7. Evaluate: sin{tan^(-1)(7/(24))} (ii) cos{cot^(-1)(5/(12))}

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  8. Solve: "cos"{cos^(-1)(x)}=0

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  9. Solve : "sin"(sin^(-1)x)=1/2

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  10. Prove the following results: cot(cos^(-1)(4/5)+sin^(-1)(4/5))=0

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  11. If a , b , c >0 and s=(a+b+c)/2, prove that tan^(-1)sqrt((2a s)/(b c...

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  12. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

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  13. If ci >0 for i=1,2,....., n prove that tan^(-1)((c1x-y)/(c1y+x))+tan^...

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  14. Evaluate: tan^(-1)(1)+tan^(-1)(0),

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  15. Prove that: sum(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2...

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  16. Sum the following series to infinity: tan^(-1)1/(1+1+1^2)+tan^(-1)1/(1...

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  17. Solve the equation: tan^-1(2x)+tan^-1 {(3x)} =pi/4

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  18. If a1,a2,a3, an are in arithmetic progression with common difference d...

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  19. Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x...

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  20. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

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