Question

If sin A - cos A=1/2 ,then find the value of sin thita +cos thita​

Answer 1

Answer:

sin thita + cos thita = √3 / √2

Step-by-step explanation:

sin A - cos A = 1/2

(sin A - cos A)^2 = sin^2A + cos^2A - 2 sinA. cosA

(1/2)^2 = sin^2A + cos^2A - 2 sinA. cosA

(1/2)^2 = 1 - 2 sinA * cosA

1/4 = 1 - 2 sinA * cosA

2 sinA * cosA = 1 - 1/2

2 sinA * cosA = 1/2

(sin A + cos A)^2 = sin^2A + cos^2A + 2 sinA. cosA

substituting value of 2 sinAcosA

(sin A + cos A)^2 = 1 + 1/2

(sin A + cos A)^2 = 3/2

taking square root both side.

(sin A + cos A) = √3 / √2

sin thita + cos thita = √3 / √2