Question

Review the incomplete derivation of the cosine sum identity.

A 2-column table with 5 rows. Column 1 has entries step 1, step 2, step 3, step 4, step 5. Column 2 has entries cosine (x + y), sine (StartFraction pi Over 2 EndFraction minus (x + y) ), blank, sine (StartFraction pi Over 2 EndFraction minus x) cosine (negative y) + cosine (StartFraction pi Over 2 EndFraction minus x) sine (negative y), blank.

Which expressions for Step 3 and Step 5 complete the derivation?

Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) – sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) – sin(x)sin(y)

Answer 1

Answer:

Option (4)

Step-by-step explanation:

STEP - 1

cos(x + y)

STEP - 2

$\text{sin}[\frac{\pi}{2}-(x+y)]$

STEP - 3

$\text{sin}[(\frac{\pi}{2}-x)-y]$

STEP - 4

$\text{sin}(\frac{\pi}{2}-x)\text{cos}(-y)+\text{cos}(\frac{\pi}{2}-x)\text{sin}(-y)$

STEP - 5

cos(x)cos(y) - sin(x)sin(y)

[Since, $\text{sin}(\frac{\pi}{2}-x)=cos(x)$ and $\text{cos}(\frac{\pi}{2}-x)=\text{sin}(x)$]

[Since, cos(-x) = cos(x) and sin(-x) = -sin(x)]

Therefore, Option (4) will be the correct option.

Answer 2

Answer:

D

Step-by-step explanation:

Top Answer was right, don't know why it was rated poorly