Q. if a sinx + b cosx = p and a cosx + b sinx = q , then. (ap - bq)² + (aq - bp)² =? given option are (1) (a² - b²) (2) (a²-b²)² (3) (a²-b²)³. (3) (a²-b²)⁴
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(ap-bq)^2+(aq-bp)^2
=a (asinx+bcosx)-b (acosx+bsinx)+a (acosx+bsinx)-b (asinx+bcosx)
=a^2sinx-b^2sinx+a^2cosx-b^2cosx
=sinx (a^2-b^2)+cosx (a^2-b^2)
=a^2-b^2
correct option is (1)(a^2-b^2)
=a (asinx+bcosx)-b (acosx+bsinx)+a (acosx+bsinx)-b (asinx+bcosx)
=a^2sinx-b^2sinx+a^2cosx-b^2cosx
=sinx (a^2-b^2)+cosx (a^2-b^2)
=a^2-b^2
correct option is (1)(a^2-b^2)
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Answer:
(a²-b²)²
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