Question

If tan teta + sin teta =m and tan teta - sin teta = n then prove that M2-n2=4 root of mn

Answer 1

Hiii friend,

Tan theta + Sin theta = M

Tan theta - Sin theta = N



LHS = (M)² - (N)²

=> (Tan²Theta+ Sin²theta)² - (Tan²Theta-Sin²theta)²

=> 4 Tan theta Sin theta

RHS = 4✓MN

=> 4 ✓(Tan theta+ Sin theta)(Tan theta-Sin theta)

=> 4 ✓ (Tan²Theta-Sin²theta)

=> 4 ✓ (Sin²theta/Cos²theta) - Sin²theta)

=> 4 × ✓Sin²thta - Sin²theta Cos²theta/Cos theta

=> 4 × Sin theta/Cos theta × ✓1-Cos² theta

=> 4 Tan theta × ✓Sin²theta

=> 4 Tan theta Sin theta = LHS

Hence,

LHS = RHS.....PROVED.....