\(\frac{1}{sinθ}-sinθ=a^3\)
\(\frac{1-sin^2θ}{sinθ}=a^3\)
\(\frac{cos^2θ}{sinθ}=a^3\)
\(a^3=\frac{cos^2θ}{sinθ}\)
\(a=\frac{cos^{2/3}θ}{sin^{1/3}θ}\)
\(a^2=\frac{cos^{4/3}θ}{sin^{2/3}θ}\) .....(1)
Similarly we can see that,
secθ - cosθ = b3
\(\frac{1}{cosθ}-cosθ=b^3\)
\(\frac{1-cos^2θ}{cosθ}=b^3\)
\(b^3=\frac{sin^2θ}{cosθ}\)
\(b=\frac{sin^{2/3}θ}{cos^{1/3}θ}\)
\(b^2=\frac{sin^{4/3}θ}{cos^{2/3}θ}\) ......(2)
From (1) and (2), we get
Hence Proved.
