Q51 of 51 Page 54

If acosx – bsinx = c. Prove that

Formula: - sin2x + cos2x = 1


Given: - acosx – bsinx = c


Let find out value of


(acosx – bsinx)2 + (asinx + bcosx)2 = a2(cos2x + sin2x) + b2(cos2x + sin2x) – 2absinxcosx + 2absinxcosx


(acosx – bsinx)2 + (asinx + bcosx)2 = a2 + b2 ……(i)


we can rewrite (i) as


(asinx + bcosx)2 = a2 + b2 – (acosx – bsinx)2




Hence, Proved.


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