Question

Solve
$\sf \: \cos ^{4} \frac{\pi}{8} + \cos ^{4} \frac{3\pi}{8} + \cos ^{4} \frac{5\pi}{8} + \cos ^{4} \frac{7\pi}{8}$

Don't give wrong answers give correct answer​

Answer 1

Answer:

cos(180-x) = -cosx

So cos(π/8) = -cos(7π/8)

And cos(3π/8) = -cos(5π/8)

There is a formula called a⁴ = (-a)⁴

Now, substitute cos(π/8) and cos(3π/8) in the place of -cos(7π/8) and -cos(5π/8)

Then you get,

2{cos²(π/8)+cos²(7π/8)}____ (1)

cos(90-x) = sinx

So, cos(7π/8) = sin(π/8) _____(2)

Substitute (2) in (1)

You get 2{1} = 2

Because cos²x+sin²x = 1

FINAL ANSWER IS 2.

PLS FOLLOW

Answer 2

Step-by-step explanation:

Answer:

cos(180-x) = -cosx

So cos(π/8) = -cos(7π/8)

And cos(3π/8) = -cos(5π/8)

There is a formula called a⁴ = (-a)⁴

Now, substitute cos(π/8) and cos(3π/8) in the place of -cos(7π/8) and -cos(5π/8)

Then you get,

2{cos²(π/8)+cos²(7π/8)}____ (1)

cos(90-x) = sinx

So, cos(7π/8) = sin(π/8) _____(2)

Substitute (2) in (1)

You get 2{1} = 2

Because cos²x+sin²x = 1

FINAL ANSWER IS 2.

PLS FOLLOW