Question

prove that (1+tan'2 theta) (1-sin theta)= 1​

Answer 1

Answer:

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Explanation:

Taking L.H.S

= (1 + tan2θ)(1 – sin θ)(1 + sin θ)

And, we know

sin2 θ + cos2 θ = 1 and sec2 θ – tan2 θ = 1

So,

L.H.S = (1 + tan2 θ)(1 – sin θ)(1 + sin θ)

= (1 + tan2 θ){(1 – sin θ)(1 + sin θ)}

= (1 + tan2 θ)(1 – sin2 θ)

= sec2 θ (cos2 θ)

= (1cos2θ1cos2θ) x cos2 θ

= 1

= R.H.S

Hence Proved