Question

If tantheta+sintheta=m and tantheta-sintheta=n then find msquare-nsquare

Answer 1

Let ¢ this symbol be theta then
To find tan¢+sin¢=m and tan¢+sin¢=n then
(m²-n²) =?
(m²-n²) = (tan¢+sin¢)²- (tan¢-sin¢)²
=4tan¢sin¢
because we know that (a+b)²-(a-b)²=4ab
Now 4tan¢sin¢ can be written as
4tan¢.√sin²¢
→4 sin¢ /cos¢.√1-cos²¢
→4.√sin²¢-sin²¢cos²¢ /cos¢
→4√(tan²¢-sin²¢)
→4√(tan¢+sin¢)(tan¢-sin¢)
4√mn
hence (m²-n²)=4√mn