Question

If alpha and beta lie in the first quadrant and sin alpha =8/17 and tan beta =5/12 , find the value of sin (alpha-beta) ,cos(alpha-beta ),and tan (alpha-beta).......plzz answer

Answer 1

Answer:

If sinα=1517sin⁡α=1517 then cosα=±817cos⁡α=±817. As αα is in the second quadrant, then the cosine shall be negative.

(I could do all the math, but 8:15:178:15:17 is a known Pythagorean triplet, and so is 5:12:135:12:13)

By the same method, we get that cosβ=−513cos⁡β=−513.

Now: sin(α+β)=sinαcosβ+cosαsinβsin⁡(α+β)=sin⁡αcos⁡β+cos⁡αsin⁡β, so we just of the values and get:

sin(α+β)=1517⋅−513+−817⋅1213=−75221+−96221=−171221sin⁡(α+β)=1517⋅−513+−817⋅1213=−75221+−96221=−171221

Also cos(α+β)=cosαcosβ−sinαsinβ=40221−180221=−140221cos⁡(α+β)=cos⁡αcos⁡β−sin⁡αsin⁡β=40221−180221=−140221.

And the tangent comes from these results: tan(α+β)=sin(α+β)cos(α+β)=171140

Answer 2

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