Question

if tan teeta plus sin teeta equal to m and tan teeta minus sin teeta equal to n then prove that m square minus n square equal to 4 root mn

Answer 1

Tan θ + sin θ = m

Tan θ - sin θ = n

PROVE THAT : m ² - n ² = 4 √ mn

SOLUTION :

m ² - n ² = ( Tan θ + sin θ )² - ( Tan θ - sin θ ) ²

= ( Tan θ + sin θ + Tan θ - sin θ) ( tan θ + sin θ - tan θ + sin θ )

= ( 2 tan θ ) ( 2 sin θ )

L. H. S. = ( 4 tanθ sin θ )

4 √mn = 4 √ tan ²θ - sin ² θ

= 4 √ { ( sin²θ / Cos²θ ) - sin²θ }

= 4 √ ( sin²θ - cos²θ sin²θ / Cos²θ )

= 4 √ sin²θ ( 1 - cos²θ ) / Cos ²θ

= 4 sin θ √sin²θ / Cos ²θ

= 4 sin θ √ tan²θ

R. H. S. = 4 sin θ tan θ

⏺️L. H. S. = R. H. S.