Answer:
The equation is not an identity.
Step-by-step 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.
