Question

4 cos cube 45 degree -3 cos 45 degree + sin 45 degree

Answer 1

Step-by-step explanation:

4cos³45°-3cos45°+sin45°

=4×(1/√2)³-3×1/√2+1/√2

=4/2√2-3/√2+1/√2

=2/√2-3/√2+1/√2

=(2-3+1)/√2

=0/√2

=0

that's your answer,I hope it will help you.

Answer 2

4cos³45° - 3cos45° + sin45° = 0

Given:

• 4cos³45° - 3cos45° + sin45°

To Find:

• Evaluate

Solution

Step 1:

Substitute cos45° = 1/√2  and sin45°= 1/√2

4cos³45° - 3cos45° + sin45°

= 4(1/√2)³ - 3(1/√2) + (1/√2)

Step 2:

Calculate the value

4/(2√2) - 2/√2

= 2√2 - 2/√2

= 0

Hence 4cos³45° - 3cos45° + sin45° = 0

Method 2:

Use identity cos3x = 4cos³x - 3cosx

4cos³45° - 3cos45° + sin45°

= cos(3 * 45°) + sin 45°

= cos (135°) + sin 45°

= cos(90° + 45°) + sin (45°)

cos (90 + x) = -sinx

= -sin(45°) +  sin (45°)

= 0

4cos³45° - 3cos45° + sin45° = 0