Question

If tanA+sinA=m and tanA-sinA=n. Show that m^2-n^2=4√mn

Answer 1

Answer:

Step-by-step explanation:

LHS :-

(tanA+sinA)²-(tanA-sinA)²

4tanAsinA               [(a+b)² - (a-b)²= 4ab]

RHS :-

4√(tanA+sinA)(tanA-sinA)

4√(tan²A-sin²A) √[sin²A/cos²A-sin²A]

4√sin²A-sin²A cos²A÷cosA

4sinA/cosA. √1-cos²A

4tanA. √sin²A cos²A÷cosA

4•sinA/cosA 1-cos²A. ✓sin²A= 4tanAsinA

LHS=RHS