Question

√2 sin (45° + A) = √2 cos (45° - A) = sin A + cos A.​

Answer 1

Correct Question :

√2 sin (45° + A) + √2 cos (45° - A) = sin A + cos A.

To find :

the value of cos A

Solution :

→ √2 sin (45° + A) + √2 cos (45° - A) = sin A + cos A

→ √2 sin 45° + sin A + √2 cos 45° – cos A = sin A + cos A

→ √ 2 sin 45° + √2 cos 45° = sin A – sin A + cos A + cos A

→ √ 2 sin 45° + √2 cos 45° = 2 cos A

We know that sin 45° is 1/√2 and cos 45° is 1/√2

$\sf \small \rightarrow \sqrt{2} \times \frac{1}{ \sqrt{2} } + \sqrt{2} \times \frac{1}{ \sqrt{2} } = 2 \: cos \: A$

$\sf \small \rightarrow1 + 1 = 2 \: cos \: A$

$\sf \small \rightarrow2 = 2 \: cos \: A$

$\sf \small \rightarrow \: cos \: A = \frac{2}{2} = 1$

• So the value of cos A is 1