Question

If sinA=cosA then find the valuee of 2tan2A+sin2A-1

Answer 1

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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.