The correct options are A sinα C cosβ α+β=π2⇒β=π2 α⇒sin (α 2 β)=sin (α+π 2α)=sin (π α)=sinα .Also, sinα = sin(π2 β) = cosβ ...

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Trigonometric Ratios of Allied Angles

If cosα+β=0...

Question

If $cos (α + β) = 0$ then $sin (α - 2 β) =$

sin α

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- sin α

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cos β

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- cos β

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Solution

The correct options are
A $sin α$
C $cos β$
$α + β = \frac{π}{2} \Rightarrow β = \frac{π}{2} - α \Rightarrow sin (α - 2 β) = sin (α + π - 2 α) = sin (π - α) = sin α$ .
Also, $sin α = sin (\frac{π}{2} - β) = cos β$

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