Express cos(sin^{-1}x-cos^{-1}y) as an algebraic expression in x and y.

lwfrgin 2020-10-27 Answered
Express cos(sin1xcos1y) as an algebraic expression in x and y.
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Expert Answer

liingliing8
Answered 2020-10-28 Author has 95 answers

Step1
Consider the given expression as cos(sin1xcos1y).
Let sin1x=α and cos1y=β, then x=sinα and y=cosβ.
Now the given expression can be write as cos(αβ).
Known formula:
l.cos(αβ)=cosαcosβ+sinαsinβ
2.sin20+cos20=1
Step 2
Compute the value of cosα and sinβ as follows.
cosα=1sin2α
=1x2
sinβ=1cos2β
=1y2
Substitute the values of cosα and sinβ in the formula (1).
cos(αβ)=cosαcosβ+sinαsinβ
=(1x2)(y)+(x)(1y2)
=x1y2+y1x2
Thus, the expression cos(sin1xcos1y) as algebraic in x and y as x 1y2+y1x2

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