Question

if sin A = cosA then the value sin ^4A +cos^4A is?

Answer 1

Answer:

Step-by-step 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.