Answer:
Here,
(cosθ + sinθ/sinθ) – (cosθ – sinθ/cosθ) = secθ cscθ
Now, Cross Multiplication
(cosθ + sinθ/sinθ) – (cosθ – sinθ/cosθ) = secθ cscθ
cosθ(cosθ + sinθ) – sinθ(cosθ – sinθ)/sinθ cosθ
cos²θ + sinθ cosθ – sinθ cosθ + sin²θ/sinθ cosθ
cos²θ + sin²θ/sinθ cosθ
Here, we know the identity
cos²θ + sin²θ = 1
So,
cos²θ + sin²θ/sinθ cosθ can be written as
1/sinθ cosθ
Here, we also know the identity
1/sinθ = cscθ
1/cosθ = secθ
1/sinθ cosθ can be written as
secθ cscθ
= L.H.S
Hence Proved!!
-TheUnknownScientist 72
