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यदि `tan (alpha +theta)=n tan (alpha-theta)`, तो सिद्ध कीजिए की- `(n+1) sin 2 theta=(n-1) sin 2 alpha` |
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Answer» दिया है- `tan (alpha+theta)=n tan (alpha-theta)` `implies (tan (alpha+theta))/(tan (alpha -theta))=n/1` `implies (tan (alpha+theta)+tan (alpha-theta))/(tan (alpha+theta)-tan (alpha-theta))=(n+1)/(n-1)` (योगान्तरानुपात विधि से) `implies ((sin (alpha+theta))/(cos (alpha+theta))+(sin (alpha-theta))/(cos (alpha-theta)))/((sin(alpha+theta))/(cos (alpha+theta))-(sin (alpha-theta))/(cos (alpha - theta)))=(n+1)/(n-1)` `implies (sin (alpha+theta)cos (alpha -theta)+cos(alpha+theta) sin (alpha-theta))/(sin (alpha+theta)cos (alpha-theta)-cos(alpha+theta)sin(alpha-theta))=(n+1)/(n-1)` `implies (sin (alpha+theta+alpha-theta))/(sin(alpha+theta-alpha+theta))=(n+1)/(n-1)` `implies (sin 2 alpha)/(sin 2 theta)=(n+1)/(n-1)` `implies (n-1) sin 2alpha=(n+1) sin 2 theta` `implies (n+1) sin 2 theta=(n-1) sin 2 alpha` |
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