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प्रश्न
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
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उत्तर
`sin^2 theta + sin theta =2`
LHS = `sin^2 theta + sin theta`
=`1- cos^2 theta + sin theta `
=`1- ( cos ^2 theta - sin theta )`
Since LHS ≠ RHS, this is not an identity.
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Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
