find  what values of x  accomplishes:sin (pi cos^2 x) + sin (`pi` sin^2 x) = 1



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pramodpandey's profile pic

Posted on (Answer #1)

Let `cos^2x=y`  , so    `sin^2x=1-y`

thus question

`sin(pi.cos^2(x))+sin(pi.sin^2(x))=1`  ,reduces to









`` where n is an integer ,let n=o







`x=69.91 `

We have taken positive only due to inverse restriction.

oldnick's profile pic

Posted on (Answer #2)

Would it go better:

sin(`pi` cos^2 x) + sin(`pi` sin^2 x)=
=2 sin (`pi` /2)  cos(`pi` cos2x)   (formula Prosthaphaeresis)

so:  2 cos(`pi` cos2x)=1     cos( `pi` cos2x)= 1/2

`pi` cos 2x =`pi` /3            `pi` cos 2x= 5`pi` /6

   cos2x = 1/3               cos2x = 5/6

x = 40° 12' 10''          x = 33°33'26''   ?


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