Establish the identity cos θ − sin 2 ⁡ θ 1 − cot 2 ⁡ θ = − sin 2 ⁡ θ

Question

Establish the identity                     cos        θ            −              sin        2            ⁡      θ              1      −              cot        2            ⁡      θ        =  −      sin    2    ⁡  θ

Dana Simmons · Accepted Answer

Identity                     cos        2            ⁡      θ      −              sin        2            ⁡      θ              1      −              cot        2            ⁡      θ        =  −      sin    2    ⁡  θ    L  .  H  .  S  ⇒                    cos        2            ⁡      (      θ      )      −              sin        2            ⁡      (      θ      )              1      −              cot        2            ⁡      (      θ      )          ⇒                    cos        2            ⁡      (      θ      )      −              sin        2            ⁡      (      θ      )              1      −                                    cos            2                    ⁡          (          θ          )                                      sin            2                    ⁡          (          θ          )                        ⇒                    cos        2            ⁡      (      θ      )      −              sin        2            ⁡      (      θ      )                      sin        2            ⁡      (      θ      )      −              cos        2            ⁡      (      θ      )        ×      sin    2    ⁡  (  θ  )    ⇒  −  (  1  )      sin    2    ⁡  (  θ  )  ⇒  −      sin    2    ⁡  (  θ  )L.H.S= R.H.S

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