Question

The general solution to cos¹⁰⁰x – sin¹⁰⁰x = 1 is ______.

Options

• `nπ + π/2`

• `nπ + π/4`

• nπ

• `nπ + π/3`

Answer 1

The general solution to cos¹⁰⁰x – sin¹⁰⁰x = 1 is nπ.

Explanation:

cos¹⁰⁰x – sin¹⁰⁰x = 1

`\implies` cos¹⁰⁰x = 1 + sin¹⁰⁰x

 Now obviously L.H.S. ≤ 1 and R.H.S. ≥ 1

`\implies` cos¹⁰⁰x = 1 + sin¹⁰⁰x = 1

`\implies` sin¹⁰⁰x = 0

`\implies` sin x = 0

`\implies` x = nπ