Question

If x = asec + btan 0 and y = a tan + bsec , prove that
(x² - y²) = (a - b).​

Answer 1

Step-by-step explanation:

We have ,

x^2 = a ^2 sec ^2 theta + b^2 tan^2 theta + 2xy sec theta • tan theta

y ^2 = a ^2 tan^2 theta + b ^2 sec ^2 theta + 2 xy sec theta tan theta

Now , x^2 - y^2 = a^2( sec ^2 theta - tan ^2 theta ) + b^2( sec^2 theta - tan ^2 theta)

= a^2 - b^2 , since sec ^2 theta - tan ^2 theta = 1

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