The Student Room Group

arcsinx+arccosx question..?

I'm not sure how to answer part d- can someone help? :s-smilie:
Reply 1
Look at the line of symmetry of the two graphs. What does it tell you about adding the y-coords of the two graphs at any value of x?
Reply 2
Original post by bobbricks
I'm not sure how to answer part d- can someone help? :s-smilie:

As an exercise, you could perform the direct evaluation of sin(sin1(x)+cos1(x))\sin(\sin^{-1}(x) + \cos^{-1}(x)) using the addition formulae for sin, and the fact that sin(cos1(x))=1x2\sin(\cos^{-1}(x)) = \sqrt{1-x^2} (which comes from letting y=cos1(x)y = \cos^{-1}(x) in sin2(y)+cos2(y)=1sin^2(y)+cos^2(y) = 1.)

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