If x = asecθ, y = atanθ, then the value of x 2 – y 2 is?
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MARK AS BRAINLIEST
Step-by-step explanation:
x−asecθ+btanθ
y=atanθ+bsecθ
Now,
x
2
−y
2
=(asecθ+btanθ)
2
−(atanθ+bsecθ)
2
=(a
2
sec
2
θ+b
2
tan
2
θ+2absecθtanθ)−(a
2
tan
2
θ+b
2
sec
2
θ+2absecθtanθ)
=a
2
sec
2
θ+b
2
tan
2
θ+2absecθtanθ−a
2
tan
2
θ−b
2
sec
2
θ−2absecθtanθ
=a
2
(sec
2
θ−tan
2
θ)−b
2
(sec
2
θ−tan
2
θ)
=a
2
∗1−b
2
∗1
=a
2
−b
2
.
Hence proved.
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