Question

The value of tan A + sin A = M and tan A - sin A = N.

The value of `("M"^2 - "N"^2) /("MN")^0.5`

Options

• 4

• 3

• 2

• 1

Answer 1

4

Explanation:

`"M"^2 - "N"^2 = ("Tan A" + "Sin A" + "Tan A" - "Sin A") ("Tan A" + "Sin A" - "Tan A" + "Sin A")`

`"M"^2 - "N"^2 = 4  "tan A sin A"`

and `("MN")^0.5 = ("tan"^2 "A" - "sin"^2 "A")^ 0.5`

`("MN")^0.5 = "sin A" [(1/("cos"^2 "A")) - 1]^0.5`

`("MN")^0.5 = "tan A sin A"`

Therefore, `("m"^2 - "n"^2)/("mn")^0.5` = 4