Question

if secA +tanA=x then prove sinA=(x2-1)/(x2+1)​

Answer 1

As we know that 1 + tan²A = sec ²A

sec²A - tan²A = 1

(secA + tan A) (secA - tanA) = 1

(secA - tanA) = 1/(secA + tanA)

secA - tanA = 1/x ( As given secA + tanA = x )

Now adding

(secA + tanA ) + ( secA - tanA) = x + 1/x

2secA = (x² + 1) /x

1/cosA = (x²+1)/2x ( As we know that secA = 1/cosA )

cosA = 2x/(x² + 1)

Cos²A = 4x²/(x² + 1)²

1 - cos²A = 1 - 4x²/(x² + 1)²

sin²A = (x² + 1 )² - 4x²/(x² + 1)² (sin²A + cos²A = 1)

sin²A = [(x²)² + 2x² + 1 -4x²]/(x² + 1)

sin²A = [(x²)² - 2x² + 1]/(x² +1)²

sinA = √(x² - 1)² / √(x² + 1)²

sinA = (x² - 1)/ (x² + 1)

Hence proved.

Answer by Syed G.M Ibrahim

Answer 2

Answer:

Step-by-step explanation: