x² − y² Without Finding θ

Introduction to Trigonometry

x² − y² Without Finding θ

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 4

The problem

If x=asec⁡θ+btan⁡θx = a\sec\theta + b\tan\theta and y=atan⁡θ+bsec⁡θ,y = a\tan\theta + b\sec\theta, prove that x2−y2=a2−b2.x^2 - y^2 = a^2 - b^2.

Step 1 · Your move

What is x2=(asec⁡θ+btan⁡θ)2x^2 = (a\sec\theta + b\tan\theta)^2?

x=asec⁡θ+btan⁡θ,x = a\sec\theta + b\tan\theta,y=atan⁡θ+bsec⁡θ\quad y = a\tan\theta + b\sec\theta
Helpful?