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Evaluate: "c o s e c"{cos^(-1)(-(12)/(13...

Evaluate: `"c o s e c"{cos^(-1)(-(12)/(13))}`

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To evaluate \( \csc(\cos^{-1}(-\frac{12}{13})) \), we can follow these steps: ### Step 1: Use the property of inverse cosine We know that: \[ \cos^{-1}(-x) = \pi - \cos^{-1}(x) \] Thus, we can rewrite our expression as: ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Evaluate: sec{sin^(-1)(-8/(17))}

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  2. Evaluate: sin{cos^(-1)(-3/5)} (ii) tan{cos^(-1)(-(12)/(13))}

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  3. Evaluate: "c o s e c"{cos^(-1)(-(12)/(13))}

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

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  5. Evaluate: "c o s e c"{cot^(-1)(-4/3)}

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

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  7. Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0-pi/2,ifx<0

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  8. Evaluate: cos{sin^(-1)(-7/(25))} (ii) sec{cot^(-1)(-5/(12))} (iii)c...

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  9. Evaluate: cot{sec^(-1)(-(13)/5)}

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  10. Evaluate: (i) tan{cos^(-1)(-7/(25))} (ii) "c o s e c"{cot^(-1)(-(12)...

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  11. Evaluate: sin{sin^(-1)(-(3)/5)+cot^(-1)(-5/(12))}

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  12. Find the value of cot(tan^(-1)a+cot^(-1)a)

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  13. If -1lt=x , ylt=1 such that sin^(-1)x+sin^(-1)y=pi/2 , find the value ...

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  14. If tan^(-1)x+tan^(-1)y=(4pi)/5, find cot^(-1)x+cot^(-1)ydot

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  15. If tan^(-1)x-cot^(-1)x=tan^(-1)(1/(sqrt(3))) find the value of xdot

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  16. If sin(cos^(-1)(5/(13))+sin^(-1)x)=1 find the value of xdot

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  17. If "sin"(sin^(-1)\ 1/5+cos^(-1)x)=1, then find the value of xdot

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  18. If cos(sin^(-1)(2/5)+cos^(-1)x)=0 find the value of xdot

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  19. Evaluate : cos(2cos^(-1)x+sin^(-1)x)a tx=1/5

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  20. If (tan^(-1) x)^2 + (cot^(-1) x)^2 = (5pi^2)/8 then x equals

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