Prove that: (sin θ – cosec θ)(cos θ – sec θ) =

Question

Philoid · Accepted Answer

To Prove: (sin - cosec)(cos- sec) =

L.H.S. = (sin θ –cosec θ)(cos θ- sec θ)

⇒

Since sin²θ + cos²θ = 1 , So

⇒

After Cancellation we get

L.H.S. = sin θ cos θ

Dividing the numerator and denominator with cos θ we get

⇒

We know

⇒

Since sec²θ = 1 + tan²θ

⇒

Dividing The Numerator and denominator by tan θ we get

⇒

Since

= R.H.S

Since L.H.S. = R.H.S

Hence Proved