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प्रश्न
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
विकल्प
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उत्तर
The given expression is
`(1+cot θ-cosec θ )(1+tan θ+sec θ)`
Simplifying the given expression, we have
`(1+cot θ-cosec θ)(1+tan θ+sec θ)`
=`(1+cos θ/sin θ-1/sin θ)(1+sin θ/cos θ+1/cos θ)`
= `(sin θ+cos θ-1)/sin θxx (cos θ+sin θ+1)/cos θ`
= `((sin θ+cos θ-1)(cos θ+sin θ+1))/(sin θcos θ)`
=`({(sin θ+cos θ)-1}{(sin θ+cos θ)+1})/(sin θ cos θ)`
=`((sin θ+cos θ)^2-(1)^2)/(sin θ cos θ)`
=`((sin θ+cos θ)^2-(1)^2)/(sin θ cos θ)`
=`((sin^2 θ+cos^2θ+2 sin θcos θ)-1)/(sin θ cos θ)`
=`((sin ^2θ+cos^2θ)+2 sinθ cos θ-1)/(sin θcos θ)`
= `(1+2 sin θ cosθ-1)/(sinθ cos θ)`
=`( 2 sin θ cos θ)/(sin θ cos θ)`
=`2`
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