Question

if sin theta + cos theta = x then find sin theta - cos theta

Answer 1

Answer:

$\huge{\underline{\underline{\sf{SoLUtiOn}}}}$

Sin θ + Cos θ = x

( Sin θ + Cos θ ) ² = x²

Sin² θ + Cos² θ + 2sin θ . cos 2 θ = x²

1 + 2Sin θ .Cos θ = x²

Sin θ × Cos θ = x² - 1 / 2 ------------(1)

Sin6 θ + Cos6 θ

= ( Sin² θ ) ³ + ( Cos² θ ) ³

= ( Sin² θ + Cos² θ ) [ ( Sin² θ ) ² + ( Cos² θ ) ² - Sin² θ .Cos² θ ) ]

= Sin⁴ θ + Cos⁴ θ - Sin² θ . Cos² θ

= ( Sin² θ + Cos² θ ) ² - 2Sin² θ . Cos² θ - Sin² θ . Cos² θ

= 1 - 3 Sin² θ . Cos² θ

= 1 - 3 ( x² - 1 / 2 ) ²

= 1 - 3 ( x² - 1 / 4 ) ²

= 4 - 3 ( x² - 1 ) ² / 4