Question

6. Find the value of
(a) cos? 18° + cos2 36° + cos²54° + cos^2 72° + cos? 90°​

Answer 1

Answer:

$\bold\red{Value=2}$

Step-by-step explanation:

${ \cos}^{2} 18 + { \cos }^{2} 36 + { \cos }^{2}54 + { \cos}^{2} 72 + { \cos }^{2} 90$

But,

we know that,

$\cos( \alpha ) = \sin(90 - \alpha )$

Therefore,

we get,

$= ( { \sin }^{2} 18 + { \cos }^{2} 18) + ( { \sin }^{2} 36 + { \cos }^{2} 36) + { \cos }^{2} 90$

But,

we know that,

${ \sin }^{2} \alpha + { \cos}^{2} \alpha = 1$

Therefore,

we get,

$= 1 + 1 + { \cos }^{2} 90 \\ \\ = 2 + { \cos}^{2}90$

But,

we know that,

$\cos(90) = 0$

Hence,

$\bold{Value=2}$