Question

……….help…..me …….pls..

Answer 1

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