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प्रश्न
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
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उत्तर
L.H.S. = \[\boxed{\text{cos}^2θ · (1 + \text{tan}^2θ)}\]
= cos2θ × \[\boxed{\text{sec}^2θ}\] ...[1 + tan2θ = \[\boxed{\text{sec}^2θ}\]]
= (cos θ × \[\boxed{\text{sec} θ}\])2
= 12
= 1
= R.H.S.
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