What will be the value of 2 cos 2 ⁡ θ − 1 , if cos 4 ⁡ θ − sin 4 ⁡ θ = 2 3 Here is my attempt: cos 4 ⁡ θ − sin 4 ⁡ θ = 2 3 ( cos 2 ⁡ θ ) 2 − ( sin 2 ⁡ θ ) 2 = 2 3 ( cos 2 ⁡ θ − sin 2 ⁡ θ ) ⋅ ( cos 2 ⁡ θ + sin 2 ⁡ θ ) = 2 3 cos ⁡ 2 θ = 2 3 But I am stuck at this step so can anyone help me ?

Question

What will be the value of   2      cos          2        ⁡  θ  −  1 , if       cos          4        ⁡  θ  −      sin          4        ⁡  θ  =      2    3  Here is my attempt:      cos          4        ⁡  θ  −      sin          4        ⁡  θ  =      2    3    (      cos          2        ⁡  θ      )          2        −  (      sin          2        ⁡  θ      )          2        =      2    3    (      cos          2        ⁡  θ  −      sin          2        ⁡  θ  )  ⋅  (      cos          2        ⁡  θ  +      sin          2        ⁡  θ  )  =      2    3    cos  ⁡  2  θ  =      2    3  But I am stuck at this step so can anyone help me ?

artirw9f · Accepted Answer

I finally got the answer  cos  ⁡  2  θ  =  2      cos          2        ⁡  θ  −  1  2      cos          2        ⁡  θ  −  1  =      2    3  This is our required answer

What will be the value of 2 cos^2 theta−1 , if cos^4 theta−sin^4 theta=2/3

Answered question

Answer & Explanation

New Questions in Trigonometry