Verify the identity tan 0 ( tan 0 + cot 0 ) = sec^2 0

Question

Verify the identity tan 0 ( tan 0 + cot 0 ) = sec^2 0

Answer 1

tanθ (tanθ + cotθ) = tan²θ + tanθ cotθ = tan²θ + 1

 

= sin²θ/cos²θ + 1 = sin²θ/cos² + cos²θ/cos² = (sin²θ + cos²θ)/cos²θ

 

= 1/cos²θ = sec²θ

Answer 2

by "0" you meant "θ" i.e. theta, which is a character available using the pulldown menu associated with Ω button.

 

By distributing tan θ; you get  tan²θ + 1 = this IS THE PYTHAGOREAN IDENTITY = square of secant of theta

 

 

I have revised this because of an horrendous error that I committed (I multiplied right side by tan theta!)

If your zeros really are zeros, then this is not an undefined expression because cot 0 has denominator sin 0 which is ÷ by 0.

Answer 3

tanθ(tanθ + cotθ) = tan²θ + tanθcotθ

 

                           = tan²θ + 1 = sec²θ