Question

If sinA = cosA, find 2tan²A + sin²A - 1

Answer 1

Given :-

sinA = cos A

sinA/cosA = 1

we know that
sinA/cosA = tan A

hence,

tan A = 1

, but we know that tan 45° = 1

hence,
A = 45°


2tan²A + sin²A -1

2tan²45° + sin²45 - 1

we know ,

tan²45° = 1 , sin²45° = 1/√2

hence ,

2(1)² + 2 × (1/√2)² - 1

2 + 1 - 1
= 2
∴ 2tan²A + sin²A -1 = 2