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Prove that: sec(tan^-1 1)+cos e c(cot^(...

Prove that: `sec(tan^-1 1)+cos e c(cot^(-1) 1)=4`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2)))

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  2. Evaluate the following: sin^(-1)(sin 10)

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  3. Prove that: sec(tan^-1 1)+cos e c(cot^(-1) 1)=4

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  4. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

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  5. Evaluate: sin(cos^(-1)3/5+cos e c^(-1)(13)/5)

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  6. Find the value of the expression sin[cot^(-1){cos (pi/2)}]

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  7. Write the value of sin{pi/3-sin^(-1)(-1/2)}

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  8. If tan^(-1)x+tan^(-1)y=pi/4, then write the value of x+y+x ydot

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  9. Prove that 2tan^(-1)(sqrt((a-b)/(a+b))tan(theta/2))=cos^(-1)((acosthet...

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  10. Solve the following equation for x : tan^(-1)(1/4)+2tan^(-1)(1/5)+...

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  11. Write the value of cos^2(1/2cos^(-1)3/5)

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  12. Write the value of sin^-1(sin1550^@)

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  13. Prove that: tan^(-1){(cos2alphasec2beta+cos2betasec2alpha)/2}=tan^(-1...

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  14. Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec^...

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  15. Show that :2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is constant for xgeq1, find...

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  16. Prove that: tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2

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  17. Simplify each of the following: cos^(-1)(3/5cosx+4/5sinx) , where -(...

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  18. Write the following functions in the simplest form: tan^(-1){x/(sqrt...

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  19. Evaluate each of the following: cot^(-1)(1/(sqrt(3)))-cos e c^(-1)(-2)...

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  20. For the principal values, evaluate the following: cot^(-1)(-1)+cos e ...

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