Asked by aleena

Prove the trigonometric identity below. Show all steps algebraically
(š‘„sinĪøāˆ’š‘¦cosĪø)2 +(š‘„cosĪø+š‘¦sinĪø)2 =š‘„2 +š‘¦2
Answered by aleena
the 2's are exponents
Answered by Joey
Someone else posted that earlier:
www.jiskha.com/questions/1866365/solve-the-following-equation-and-state-the-general-solution-for-all-values-of-x-in-exact

Answered by mathhelper
Not the same question, so here it goes

prove: (š‘„sinĪøāˆ’š‘¦cosĪø)^2 +(š‘„cosĪø+š‘¦sinĪø)^2 =š‘„^2 +š‘¦^2

Let x = sinA and let y = cosA

Left Side = (š‘„sinĪøāˆ’š‘¦cosĪø)^2 +(š‘„cosĪø+š‘¦sinĪø)^2
= (sinAsinĪø - cosAcosĪø) + (sinAcosĪø + cosAsinĪø)^2
= ( cos(A+Īø))^2 + (sin(A+Īø))^2
= 1

RS = (sinA)^2 + (cosA)^2
= 1
= LS

Answered by oobleck
clever solution, but if |x| or |y| >1 then they cannot be sin and cos of A. In that case, some more algebra will be needed, but it still works out to x^2 + y^2.
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