Question

The expression ${\cos }^2(\varphi +b)+{\cos }^2(\varphi +a+b)+{\cos }^{2}a-2\cos a.\cos (\varphi +b).\cos (\varphi +a+b)$ is independent of

• A. $a$
• B. $b$
• C. $\varphi$
• D. $a$ and $b$ only

Answer 1

Answer: (A), (B), (C)

The correct options are
A $a$
B $b$
C $\varphi$

Given expression

${\cos }^2(\varphi +b)+{\cos }^2(\varphi +a+b)+{\cos }^{2}a-\left[\cos \right(\varphi +b+a)+\cos (\varphi +b-a\left)\right]\cos (\varphi +a+b)$

$\Rightarrow {\cos }^2(\varphi +b)+{\cos }^{2}a-\cos (\varphi +b-a)\cos (\varphi +b+a)$

$\Rightarrow {\cos }^2(\varphi +b)+{\cos }^{2}a-\left[{\cos }^2\right(\varphi +b)-{\sin }^{2}a]=1$