Question

If tan + sin = m and tan - sin =n, show that [m^2-n^2]2= 16 mn solutions

Answer 1

Step-by-step explanation:

LHS

=(m²-n²)²

=[(tan+sin)²-(tan-sin)²]²

=[tan²+2tan.sin+sin²-tan²+2tan.sin-sin²]²

=[4tansin]²

=16tan²sin²

=16[tan²(1-cos²)]

=16[tan²-tan²cos²]

=16[tan²-sin²]

=16(tan+sin)(tan-sin)

=16mn