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प्रश्न
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity:
L.H.S. = cotθ + tanθ
= `square/sin theta xx sin theta/cos theta`
= `(square + square)/(sin theta * cos theta)`
= `1/(sin theta * cos theta)` ...(∵ sin2θ + cos2θ = 1)
= `1/sin theta xx 1/cos theta`
= `square xx sec theta`
∴ L.H.S. = R.H.S.
∴ cotθ + tanθ = cosecθ × secθ
कृती
बेरीज
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उत्तर
L.H.S. = cotθ + tanθ
= \[\frac{\boxed{\text{cosθ}}}{\text{sinθ}}\] `xx sin theta/cos theta`
= \[\frac{\boxed{\text{cos}^2 θ} + \boxed{\text{sin}^2θ}}{\text{sin θ . cos θ}}\]
= `1/(sin theta * cos theta)` (∵ sin2θ + cos2θ = 1)
= `1/sin theta xx 1/cos theta`
= \[\boxed{\text{cosec θ}}\] × secθ
∴ L.H.S. = R.H.S.
∴ cotθ + tanθ = cosecθ × secθ
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