Question

prove that tan 0/sec 0 -1=
sec 0 +1/tan o​

Answer 1

Answer:

Step-by-step explanation:

tanθ/secθ -1

= sinθ/cosθ/secθ - 1

= sinθ/cosθ(secθ - 1)

= sinθ / 1 - cosθ

multiply numerator and denominator by 1 + cosθ

= sinθ(1+cosθ)/ (1 -cosθ)(1+cosθ)

= sinθ(1+cosθ) / 1 - cos²θ

= sinθ(1+cosθ)/ sin²θ  (∵ 1 - cos²θ  = sin²θ )

= 1 + cosθ/ sinθ

take cosθ common in the numerator

= cosθ(1/cosθ + 1) / sinθ

=  (1/cosθ + 1) / (sinθ/cosθ)

= secθ + 1 / tanθ

= R.H.S.

Hence proved.