The value of the expression cos 4 (π/8)+ cos 4 (3 π/8)+ cos 4 (5 π/8)+ cos 4 (7 π/8)=

Question

The value of the expression cos 4 (π/8)+ cos 4 (3 π/8)+ cos 4 (5 π/8)+ cos 4 (7 π/8)= (A) 1 (B) 2 (C) (3/2) (D) 4

Tardigrade Admin · Accepted Answer

cos 4 (π/8)+ cos 4 (3 π/8)+ cos 4 (5 π/8)+ cos 4 (7 π/8) =2( cos 4 (π/8)+ sin 4 (π/8))=2[( cos 2 (π/8)+ sin 2 (π/8))2-2 cos 2 (π/8) sin 2 (π/8)] =2(1-(1/4))=(3/2)

Q. The value of the expression $cos^{4} \frac{π}{8} + cos^{4} \frac{3 π}{8} + cos^{4} \frac{5 π}{8} + cos^{4} \frac{7 π}{8} =$

1

2

$\frac{3}{2}$

4

$cos^{4} \frac{π}{8} + cos^{4} \frac{3 π}{8} + cos^{4} \frac{5 π}{8} + cos^{4} \frac{7 π}{8}$
$= 2 (cos^{4} \frac{π}{8} + sin^{4} \frac{π}{8}) = 2 [(cos^{2} \frac{π}{8} + sin^{2} \frac{π}{8})^{2} - 2 cos^{2} \frac{π}{8} sin^{2} \frac{π}{8}]$
$= 2 (1 - \frac{1}{4}) = \frac{3}{2}$

Q. The value of the expression cos48π​+cos483π​+cos485π​+cos487π​=

1

2

23​

4

cos48π​+cos483π​+cos485π​+cos487π​ =2(cos48π​+sin48π​)=2[(cos28π​+sin28π​)2−2cos28π​sin28π​] =2(1−41​)=23​

Q. The value of the expression $cos^{4} \frac{π}{8} + cos^{4} \frac{3 π}{8} + cos^{4} \frac{5 π}{8} + cos^{4} \frac{7 π}{8} =$

$\frac{3}{2}$

$cos^{4} \frac{π}{8} + cos^{4} \frac{3 π}{8} + cos^{4} \frac{5 π}{8} + cos^{4} \frac{7 π}{8}$
$= 2 (cos^{4} \frac{π}{8} + sin^{4} \frac{π}{8}) = 2 [(cos^{2} \frac{π}{8} + sin^{2} \frac{π}{8})^{2} - 2 cos^{2} \frac{π}{8} sin^{2} \frac{π}{8}]$
$= 2 (1 - \frac{1}{4}) = \frac{3}{2}$