Question

The expression $co{s}^2\phi +co{s}^2(\alpha +\phi )-2cos\alpha cos\phi cos(\alpha +\phi )$ is independent of

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$co{s}^2\phi +co{s}^2(\alpha +\phi )-\left[cos\right(a+\phi )+cos(a-\phi \left)\right]cos(a-\phi )=co{s}^2\phi -cos(a+\phi )cos(a-\phi )=co{s}^2\phi -(co{s}^2\phi -sin2a)=si{n}^{2}a$ which is independent of $\phi$