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