Question

Prove that sec²∅ - cot²(90⁰ - ∅) = cos² (90⁰ - ∅) + cos²∅

Answer 1

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Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

L.H.S = sec² (θ)−cot² (θ)(90−θ)

= sec² (θ)−tan² (θ)

= 1 / cos² (θ) - sin² (θ) / cos² (θ)

= (−sin² (θ)) / (cos² (θ)

(cos²(θ) / (cos²(θ) = 1

R.H.S = cos² (90−θ) + cos²θ)

sin²(θ) + cos² (θ) = 1

L.H.S = R.H.S