Rs aggarwal Identities. Ex7a. Q. 7
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L.H.S= {sinΘ÷(1+cosΘ)}+{(1+cosΘ)÷sinΘ}
=sinΘ×sinΘ+(1+cosθ)²÷(1+cosΘ)×sinΘ
=(sin²Θ+1+cos²Θ+2cosΘ)÷{(1+cosΘ)×(sinΘ)} (Since sin²Θ+cos²Θ=1)
=(1+1+2cosΘ)÷{(1+cosΘ)(sinΘ)}
=2(1+cosΘ)÷{(1+cosΘ)(sinΘ)}
=2÷sinΘ (Since 1÷sinΘ=cosecΘ)
=2cosecΘ= R.H.S
=sinΘ×sinΘ+(1+cosθ)²÷(1+cosΘ)×sinΘ
=(sin²Θ+1+cos²Θ+2cosΘ)÷{(1+cosΘ)×(sinΘ)} (Since sin²Θ+cos²Θ=1)
=(1+1+2cosΘ)÷{(1+cosΘ)(sinΘ)}
=2(1+cosΘ)÷{(1+cosΘ)(sinΘ)}
=2÷sinΘ (Since 1÷sinΘ=cosecΘ)
=2cosecΘ= R.H.S
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