(Sine-cose)

(Sine+cose)

+

(Sine+cose) 2

(Sine-cose) (2Sin²0-1)​

1 thought on “(Sine-cose)<br /><br />(Sine+cose)<br /><br />+<br /><br />(Sine+cose) 2<br /><br />(Sine-cose) (2Sin²0-1)​”

1. Step-by-step explanation:

   sinθ+cosθ=

   2

   cosθ

   To prove:- cosθ+sinθ=

   2

   sinθ

   Proof:-

   sinθ+cosθ=

   2

   cosθ

   Squaring both sides, we get

   sin

   2

   θ+cos

   2

   θ+2sinθcosθ=2cos

   2

   θ

   ⇒sin

   2

   θ−cos

   2

   θ+2sinθcosθ=0

   Subtracting 2sin

   2

   θ both sides, we have

   −sin

   2

   θ−cos

   2

   θ+2sinθcosθ=−2sin

   2

   θ

   sin

   2

   θ+cos

   2

   θ−2sinθcosθ=2sin

   2

   θ

   (cosθ−sinθ)

   2

   =2sin

   2

   θ

   ⇒cosθ−sinθ=

   2

   sinθ

   Hence proved.

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