Question

Prove the following:

`1/(tan⁡ theta + cot theta) = sin theta.cos⁡ theta`

Answer 1

`tanθ = sinθ/cosθ`

`cotθ = cosθ/sinθ`

Substitute these into the denominator:

`tanθ + cotθ = sinθ/cosθ + cosθ/sinθ`

`(sinθ(sinθ) + cosθ(cosθ))/(sinθ.cosθ) = (sin^2θ + cos^2θ)/(sinθ.cosθ)`

sin²θ + cos²θ = 1

∴ `1/(sinθ.cosθ)`

`1/(tanθ + cotθ) = 1/(1/(sinθ.cosθ))`

sinθ.cosθ