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  • If cos (α + β) = 0, then sin (α – β) can be reduced to (A) cos β (B) cos 2β (C) sin α (D) sin 2α

If cos (α + β) = 0, then sin (α – β) can be reduced to

(A) cos β                     (B) cos 2β                    (C) sin α                      (D) sin 2α

Answers (1)

\\\text{Given that }\cos(\alpha+\beta)=0\\\Rightarrow (\alpha+\beta)=90^0...........(1)\\\text{wehave to find }\sin(\alpha-\beta)\\\text{from(1) we can write }\alpha=90-\beta\\\therefore \ \sin(\alpha-\beta)=\sin(90-\beta-\beta)\\=\sin(90-2\beta)=\cos2\beta \\(\text{since sin(90-x)=cosx})

Hence option B is correct.

Posted by

infoexpert27

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