derivation of sin theta plus cos theta by root under of 1 plus sin 2 theta
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sin theta plus cos theta ÷ root under of 1 plus sin 2 theta
sin theta plus cos theta ÷ root under of (sin theta plus cos theta) plus sin 2 theta
sin theta plus cos theta ÷ root under of (sin^2theta plus cos^2theta) plus 2* sin theta* cos theta
sin theta + cos theta ÷ root under of (sin theta + cos theta)^2
sin theta + cos theta ÷ (sin theta + cos theta)
= 1
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