JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Let \({f_k}\,(x)\, = \frac{1}{k}({\sin ^k}\,x\, + \,{\cos ^k}\,x)\) for \(k=1,2,3,...\) Then for all \(x \in R,\) the value of \(f_4(x) - f_6 (x)\) is equal to
- A \(\frac {1}{12}\)
- B \(\frac {1}{4}\)
- C \(\frac {-1}{12}\)
- D \(\frac {5}{12}\)
Answer & Solution
Correct Answer
(A) \(\frac {1}{12}\)
Step-by-step Solution
Detailed explanation
\({F_4}(x)\, = \,\frac{{{{\sin }^4}x + {{\cos }^4}x}}{4} = \) \(\frac{{1 - 2{{\sin }^2}x.{{\cos }^2}x}}{4} = \frac{1}{4} - \frac{1}{2}{\sin ^2}x.{\cos ^2}x\) \({F_6}(x)\, = \,\frac{{{{\sin }^6}x + {{\cos }^6}x}}{6} = \)…
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