Let α , β be such that π

Question

Let α , β be such that π < α − β < 3 π . If sin α + sin β = − 65 21 ​ and cos α + cos β = − 65 27 ​ , then the value of cos 2 α − β ​ is

TestHub · Accepted Answer

sin α + sin β = − 65 21 ​ and cos α + cos β = − 65 27 ​ . Squaring and adding, we get ​ 2 + 2 cos ( α − β ) = ( 65 ) 2 1170 ​ ⇒ cos 2 ( 2 α − β ​ ) = 130 9 ​ ⇒ cos ( 2 α − β ​ ) = 130 ​ − 3 ​ ( ∵ 2 π ​ < 2 α − β ​ < 2 3 π ​ ) . ​

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