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What is the principal value of sin^(-1)(...

What is the principal value of `sin^(-1)(-(sqrt(2))/2)?`

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Let, x=`sin^(-1)(-(sqrt(2))/2)`
the principal value of `sin^(−1)x ` lies in `[ −π/2​,π/2​]`
`=> sinx=1/sqrt(2)​`
`=> x=π/4`​
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
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  5. If tan^(-1)(sqrt(3))+cot^(-1)x=pi/2,t h e nfin dxdot

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  6. If sin^(-1)(1/3)+cos^(-1)x=pi/2,then find x

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  7. Write the value of 2sin^(-1)\ 1/2+cos^(-1)((a-b)/(a+b))

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  8. Evaluate: sin^(-1)(s in(3pi)/5)

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  9. If (tan^(-1)x)^(2)+(cot^(-1)x)^(2)=(5 pi^(2))/(8), then the value of x...

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

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

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

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

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

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