Question

In $A_n={\cos }^n\theta +{\sin }^n\theta ,nϵN$ and $\theta ϵR$

The value of $2A_6-3A_4+5$ is equal to

• A. $4$
• B. $9$
• C. $6$
• D. $15$

Answer 1

The correct option is A $4$

$A_n={\cos }^n\theta +{\sin }^n\theta A_6={\cos }^6\theta +{\sin }^6\theta =1-3{\sin }^2\theta {\cos }^2\theta =1-\frac{3}{4}{\sin }^{2}2\theta A_4={\cos }^4\theta +{\sin }^4\theta =1-2{\sin }^2\theta {\cos }^2\theta =1-\frac{1}{2}{\sin }^{2}2\theta 2A_6-3A_4+5=2-\frac{3}{2}{\sin }^{2}2\theta -3+\frac{3}{2}{\sin }^{2}2\theta +5=4$