Prove the following trigonometric identities:cotθ - tanθ =\(\frac{2c

1.	Prove the following trigonometric identities:cotθ - tanθ =\(\frac{2cos^2θ-1}{sinθ.cosθ}\)
Answer» L.H.Scotθ - tanθ =\(\frac{cosθ}{sinθ}-\frac{sinθ}{cosθ}\) =\(\frac{cos^2θ-sin^2θ}{sinθ.cosθ}\) =\(\frac{cos^2θ-(1-cos^2θ)}{sinθ.cosθ}\) =\(\frac{cos^2θ-1+cos^2θ)}{sinθ.cosθ}\) = \(\frac{2cos^2θ-1}{sinθ.cosθ}\) = R.H.S Hence Proved.

Prove the following trigonometric identities:cotθ - tanθ =\(\frac{2cos^2θ-1}{sinθ.cosθ}\)

Answer»

L.H.Scotθ - tanθ =\(\frac{cosθ}{sinθ}-\frac{sinθ}{cosθ}\)

=\(\frac{cos^2θ-sin^2θ}{sinθ.cosθ}\)

=\(\frac{cos^2θ-(1-cos^2θ)}{sinθ.cosθ}\)

=\(\frac{cos^2θ-1+cos^2θ)}{sinθ.cosθ}\)

= \(\frac{2cos^2θ-1}{sinθ.cosθ}\)

= R.H.S

Hence Proved.