Question

PROVE THE FOLLOWING TRIGONOMETRIC IDENTITIES:

1. cot-tan = 2cos^2-1/sin×cos
2. tan-cot = 2cos^2-1/sin×cos​

Answer 1

1.

cotθ−tanθ

=

sinθ

cosθ

−

cosθ

sinθ

=

cosθ.sinθ

cos

2

θ−sin

2

θ

=

sinθ.cosθ

2cos

2

θ−1

. [Since 1−sin

2

θ=cos

2

θ]