Question

Determine whether the equation is an identity or not an identity. Sin theta/cos theta + cos theta/sin theta = cos theta sin theta

Answer 1

The equation is not an identity.

Explanation:

Since we have Sin theta/cos theta + cos theta/sin theta = cos theta sin theta, we re-write as Sinθ/cosθ + cosθ/sinθ = cosθsinθ where theta = θ.

For the equation to be an identity, we need to show that L.H.S(left-hand-side)= R.H.S (right-hand-side)

So,

Sinθ/cosθ + cosθ/sinθ = (Sin²θ + cos²θ)/cosθsinθ (taking L.C.M = cosθsinθ)

= 1/cosθsinθ (Sin²θ + cos²θ = 1)

≠ cosθsinθ

Since L.H.S = Sinθ/cosθ + cosθ/sinθ = 1/cosθsinθ ≠ R.H.S = cosθsinθ, the equation is not an identity.