If x = p secA cosB, y = q secA sinB, and z = r tanA, what is the value of (x²)/(p²)+(y²)/(q²)-(z²)/(r²) ?

If x = p secA cosB, y = q secA sinB, and z = r tanA, what…

If x = p secA cosB, y = q secA sinB, and z = r tanA, what is the value of $\frac{x^2}{p^2}+\frac{y^2}{q^2}-\frac{z^2}{r^2}$ ?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 1.

x = p secA cosB, y = q secA sinB, and z = r tanA

The value of $\frac{x^2}{p^2}+\frac{y^2}{q^2}-\frac{z^2}{r^2}$

⇒ $\frac{(p secA cosB)^2}{p^2}+\frac{(q secA sinB)^2}{q^2}-\frac{(r tanA)^2}{r^2}$

⇒ $\frac{p^2 sec^2A cos^2B}{p^2}+\frac{q^2 sec^2A sin^2B}{q^2}-\frac{r^2 tan^2A}{r^2}$

⇒ sec²A cos²B + sec²A sin²B - tan²A [cos²A + sin²A = 1]

⇒ sec²A (cos²B + sin²B) - tan²A

⇒ sec²A - tan²A = 1