Question

If sinA-cosA then find the value of sin^4A+cos^4A

Answer 1

sinA-cosA=1
Squaring both sides,
(sinA-cosA)²=1
or, sin²A-2sinAcosA+cos²A=1
or, sin²A+cos²A-2sinAcosA=1
or, 1-2sinAcosA=1
or, -2sinAcosA=1-1
or, sinAcosA=0 --------------------(1)
sin⁴A+cos⁴A
=(sin²A)²+(cos²A)²
=(sin²A+cos²A)²-2sin²Acos²A
=1²-2(sinAcosA)²
=1-2(0)² [Using (1)]
=1 Ans.

Answer 2

Answer:

Explanation:

sinA-cosA=1

Squaring both sides,

(sinA-cosA)²=1

or, sin²A-2sinAcosA+cos²A=1

or, sin²A+cos²A-2sinAcosA=1

or, 1-2sinAcosA=1

or, -2sinAcosA=1-1

or, sinAcosA=0 --------------------(1)

sin⁴A+cos⁴A

=(sin²A)²+(cos²A)²

=(sin²A+cos²A)²-2sin²Acos²A

=1²-2(sinAcosA)²

=1-2(0)² [Using (1)]

=1 Ans.