Question

$Ifco{s}^{4}A–si{n}^{4}A=\frac{3}{5},then2co{s}^{2}A–1=?$

• A. 4/5
• B. 3/4
• C. 4/3
• D. 0
• E. 3/5

Answer 1

The correct option is E

3/5

We know sin${}^2$A + cos${}^2$A = 1 and a${}^2$ - b${}^2$ = (a+b) (a-b)

Using the two identities, we have cos${}^4$A - sin${}^4$A = (cos${}^2$A - sin${}^2$A) (sin${}^2$A + cos${}^2$A) = (2 cos${}^2$A - 1) $\times$ 1 = $\frac{3}{5}$