Question

If tan a +sin a = m and tan a-sin a= n show that (m)2 -(n)2 =4√mn

Answer 1

mn=(tan a+sin a)(tan a -sin a)
=tan²a -sin²a
rooting both sides.
√mn=√tan²a-sin²a .....(1)
..
..
m²-n²
=(tan a + sin a)² - (tan a- sin a)²
=[tan²a+sin²a+2tan a×sin a]-[tan²a+sin²a-2tan a×sin a]
=tan²a+sin²a+2tan a ×sin a-tan²a-sin²a+2tan a×sin a
=(2×tan a×sin a) +(2×tan a×sin a)
=4 tan a.sin a