( sin ⁡ 4 θ ) can be written as:A) 4 sin ⁡ θ ( 1 − 2 sin 2 ⁡ θ ) ( 1 − sin 2 ⁡ θ )B) 2sinθcosθsin2θ C) 4sinθ–6sin3θ D) None of these

Question

(  sin  ⁡  4  θ  ) can be written as:A)   4  sin  ⁡  θ  (  1  −  2      sin    2    ⁡  θ  )  (      1    −          sin      2        ⁡    θ    )B) 2sinθcosθsin2θ C) 4sinθ–6sin3θ D) None of these

nelagodafsed · Accepted Answer

The correct answer is A  4  sin  ⁡  θ  (  1  −  2      sin    2    ⁡  θ  )  (      1    −          sin      2        ⁡    θ    )Explanation for correct option:Simplifying the equations using trigonometric identities:Given expression is: (sin4θ)Expanding the expression:sin4θ=sin2(2θ)Using the formula sin2A=2sinAcosA we get:sin4θ=2sin2θcos2θUsing the formula cos2θ=1–2sin2θ we get:sin4θ=2(2sinθcosθ)(1–2sin2θ)=4sinθ(1–2sin2θ)(cosθ)Using the identity sin2A+cos2A=1 we get:  sin  ⁡  4  θ  =  4  ∈  θ  (  1  −  2      ∈    2    θ  )  (      1    −          sin      2        ⁡    θ    )Thus, the correct answer is answer (A).

(sin 4 theta) can be written as: ?

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