if tan theta = sin alpha - cos alpha / sin alpha + cos alpha , then show that sin - Maths - Trigonometric Functions

Question

if tan theta = sin alpha - cos alpha / sin alpha + cos alpha , then
show that sin alpha + cos alpha = root 2 cos theta​

Simranpreet Singh · Accepted Answer

Hi, recently I had given the following answer to the same question
to a another student: Please go through it;
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ana_qa_image_57e27b4867df4%20jpeg">

if tan theta = sin alpha - cos alpha / sin alpha + cos alpha , then show that sin alpha + cos alpha = root 2 cos theta​

if tan theta = sin alpha - cos alpha / sin alpha + cos alpha , then show that sin alpha + cos alpha = root 2 cos theta