Question

If secx + tanx = p and secx - tanx= q then what is value of p square - q square .

Answer 1

Step-by-step explanation:

All steps are explained in photo

Answer 2

Given :

• sec x + tan x = p

• sec x - tan x = q

To Find :

• Value of p² - q²

Solution :

By using identity :

$\large\implies\boxed{\sf {a}^{2} - {b}^{2} = (a + b)(a - b)}$

Now

$\implies \sf{p}^{2} - {q}^{2} ={( \sec x + \tan x)}^{2} -{( \sec x - \tan x)}^{2} \\ \\\implies \sf({ \sec}^{2}x + { \tan}^{2}x+ 2 \sec x.\tan x) -({ \sec}^{2}x+{\tan}^{2}x - 2 \sec x.\tan x) \\ \\ \implies \sf{ \sec}^{2}x+ { \tan}^{2}x + 2 \sec x.\tan x-{ \sec}^{2}x- { \tan}^{2}x + 2 \sec x.\tan x\\ \\\implies \sf 4 \sec x.\tan x \\ \\ \implies \sf4 \times \frac{1}{ \cos x} \times \frac{ \sin x}{ \cos x} \\ \\\large\implies\boxed {\boxed {\frac{\sf 4\sin x}{{\sf\cos}^2 x}}}$