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

Evaluate the following: `sin^(-1)(sin 10)`

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To evaluate the expression \( \sin^{-1}(\sin 10) \), we need to follow these steps: ### Step 1: Understand the Range of the Inverse Function The function \( \sin^{-1}(x) \) (also known as arcsin) has a range of \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \) or approximately \( [-1.57, 1.57] \) radians. Since \( 10 \) radians is outside this range, we cannot directly apply the inverse sine function. **Hint:** Always check the range of the inverse trigonometric function before applying it. ### Step 2: Convert Radians to Degrees ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Evaluate: sin(cot^(-1)x) (ii) cos(tan^(-1)x)

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  2. Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2)))

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

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  4. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(s...

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

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

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  7. Find the value of the expression sin[cot^(-1){cos(tan^-1 1)}]

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

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

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

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

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

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

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

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

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

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

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

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

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

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