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Evaluate: (i) tan{cos^(-1)(-7/(25))} (i...

Evaluate: (i) `tan{cos^(-1)(-7/(25))}` (ii) `"c o s e c"{cot^(-1)(-(12)/5)}`

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Let's evaluate the given expressions step by step. ### (i) Evaluate \( \tan(\cos^{-1}(-\frac{7}{25})) \) 1. **Let \( \theta = \cos^{-1}(-\frac{7}{25}) \)**: - This means \( \cos(\theta) = -\frac{7}{25} \). 2. **Determine the range of \( \theta \)**: ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If (tan^(-1)x)^(2)+(cot^(-1)x)^(2)=(5 pi^(2))/(8), then the value of x...

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  2. Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

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

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

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  5. If -1lt=x , ylt=1 such that sin^(-1)x+sin^(-1)y=(2pi)/3, find the valu...

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

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

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

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

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

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  11. Let f(x)=e^(cos^(-1){sin(x+pi/3)}) Then, f((8pi)/9)= (a)e^(5pi//18...

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  12. If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4- u/...

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  13. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  14. If alpha=tan^(-1)(t a n(5pi)/4)a n dbeta=tan^(-1)(-tan(2pi)/3),t h e n...

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  15. The domain of cos^(-1)(x^2-4) is (a) [3,5] (b) [-1,1] (c)[-sqrt(5),-...

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  16. In a A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1...

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  17. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

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  18. Solve the following equations: sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]...

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  19. Solve the equation of x:sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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  20. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

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