Question

root 2 Cos pi by 4 minus A is equals to Cos A + sin a prove that​

Answer 1

Proof:

Now, L.H.S. = √2 cos(π/4 - A)

= √2 [ cos(π/4) cosA + sin(π/4) cosA ]

= √2 [ 1/√2 * cosA + 1/√2 * cosA ]

= √2 / √2 ( cosA + sinA)

= cosA + sinA = R.H.S.

Hence, proved.

Trigonometric rules:

1. sin(A + B) = sinA cosB + cosA sinB

2. sin(A - B) = sinA cosB - cosA sinB

3. cos(A + B) = cosA cosB - sinA sinB

4. cos(A - B) = cosA cosB + sinA sinB

5. sin(π/4) = cos(π/4) = 1/√2

Answer 2

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