Question

If tan Φ + sin Φ = m, and tan Φ-sin Φ=n, find the value of sinΦ*cosΦ.​

Answer 1

Answer:-

Let Φ = A.

Given:

tan A + sin A = m -- equation (1)

tan A - sin A = n -- equation (2).

Add equations (1) & (2).

→ tan A + sin A + tan A - sin A = m + n

→ 2tan A = m + n

→ tan A = (m + n) / 2

Putting the value of tan A in equation (1) we get,

→ (m + n) / 2 + sin A = m

→ sin A = m - (m + n) / 2

→ sin A = (2m - m - n) / 2

→ sin A = (m - n) / 2

• tan A = sin A/cos A

Hence,

→ sin A/cos A = (m + n) / 2

→ 1/cos A * (m - n) / 2 = (m + n) / 2

→ cos A = [ (m + n) / 2 ] * (2 / m - n )

→ cos A = m + n / m - n

Now,

→ sin A * cos A = (m - n) / 2 * (m + n) / (m - n)

→ sin A * cos A = (m - n)(m + n) / 2 * (m - n)

→ sin A * cos A = (m + n) / 2

Answer 2

Answer:

Sorry dear,

Step-by-step explanation:

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