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प्रश्न
If cos θ = `3/5` , show that `((sin theta - cot theta ))/(2tan theta)=3/160`
उत्तर
LHS = `((sin theta - cot theta ))/(2tantheta)`
=`(sin theta costheta /sintheta )/(2(sintheta/costheta))`
=`((sin^2theta - costheta)/sintheta)/((2 sintheta/costheta))`
=` (costheta(sin^2theta-costheta))/(2sin^2theta)`
=`(costheta (1-cos^2theta-costheta))/(2(1-cos^2theta))`
=`(3/5[1-(3/5)^2-3/5])/(2[1-(3/5)^2])`
=`(3/5(1/1-9/25-3/5))/(2(1-9/25))`
=`(3/5((25-9-15)/25))/(2((25-9)/25))`
=`(3/5(1/25))/(2(16/25))`
=`3/(5xx2xx16)`
=`3/160`
= RHS
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