If cosA+sinA=5/4, find tanA.
Show answer & explanation
Correct answer: A
Explanation
Has been given :
cosA + sinA = 5/4
According to the formula:
(cosA + sinA)² = cos²A + sin²A + 2sinAcosA
(5/4)² = 1 + 2sinAcosA
25/16 = 1 + 2sinAcosA
2sinAcosA = 25/16 − 1
= 25/16 − 16/16
= 9/16
sinAcosA = 9/32
tanA = sinA / cosA
assume
sinA = x, cosA = y
x + y = 5/4
xy = 9/32
tanA = x/y
tanA = (5 − √7) / (5 + √7)