Question

If 2x = secA and 2/x = tanA, prove that (x2 – 1/x2) = ¼​

Answer 1

Answer:

secA = 2x -----( 1 )

tanA = 2/x ------( 2 )

sec² A - tan² A = 1

( 2x )² - ( 2 /x )² = 1

4x² - 4/x² = 1

4 ( x² - 1/ x² ) = 1

2( x² - 1/ x² ) = 1/2

I hope this helps you.

Answer 2

Formula:-

$\underline\green{\boxed{\bf sec²θ−tan²θ=1}}$

Substitute the given values in terms of x.

$\implies\sf (2x)^{2} -\bigg(\dfrac{2}{x}\bigg)^{2} = 1 \\\\\implies4x^{2} -\dfrac{4}{x^{2} }=1 \\\\\implies4\bigg(x^{2} -\dfrac{1}{x^{2} } \bigg) = 1\\\\\implies x^{2} -\dfrac{1}{x^{2} } =\dfrac{1}{4}$

Hope it helps