Question

Sin^6θ + Cos^6θ = Cot² θ + Cot⁴ θ​

Answer 1

Step-by-step explanation:

To prove :

sin 6 θ+cos

6 θ=1−3sin 2 θcos 2 θLHS sin 6 θ+cos 6 θ=(sin 2 θ) 3 +(cos 2θ) 3 =(sin) 2 θ+cos 2 θ)(sin)4 θ+cos 4 θ−sin 2 θcos 2 θ)[a 3 +b 3 =(a+b)(a 2 +b 2 −ab)]=1(sin 4 θ+cos 4θ−sin2

θcos 2θ)(∵sin 2 x+cos 2 x=1)=(sin 2 θ+cos 2θ) 2−2sin 2 θcos 2 θ−sin 2θcos 2 θb((a+b) 2 −2ab=a 2 +b 2 )=(1−3sin 2 θcos 2 θ)= R.H.S