Convert the expression. $\cos ^ { 4 } b - \sin ^ { 4 } b$
A)2 cos b
B) cos 2b
C) cos b
D)2 cos 2b
E) 4 cos b

Question

Convert the expression.   $\cos ^ { 4 } b - \sin ^ { 4 } b$  
A)2 cos b
B) cos 2b
C) cos b
D)2  cos 2b
E) 4 cos b

Quizplus · Accepted Answer

This expression can be simplified using the trigonometric identities. First, recognize that it resembles the difference of squares formula, $a^2 - b^2 = (a + b)(a - b)$. Applying this to the given expression, we get $(\cos^2 b + \sin^2 b)(\cos^2 b - \sin^2 b)$. Since $\cos^2 b + \sin^2 b = 1$, the expression simplifies to $\cos^2 b - \sin^2 b$, which is the definition of $\cos 2b$.

Convert the Expression cos⁡4b−sin⁡4b\cos ^ { 4 } b - \sin ^ { 4 } bcos4b−sin4b

Convert the Expression $\cos ^ { 4 } b - \sin ^ { 4 } b$