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\frac { \operatorname { cot } \alpha \cdot \operatorname { cos } \alpha } { \operatorname { cot } \alpha + \operatorname { cos } \alpha } = \frac { \operatorname { cot } \alpha - \operatorname { cos } \alpha } { \operatorname { cot } \alpha \cdot \operatorname { cos } \alpha } |
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Answer» CotAcosA/cotA+cosA=[(cosA/sinA)cosA]/[(cosA/sinA)+cosA]=(cos²A/sinA)/[(cosA+sinAcosA)/sinA]=cos²A/cosA(1+sinA)=cosA/(1+sinA)=[cosA(1-sinA)]/[(1+sinA)(1-sinA)][multiplying the numerator and the denominator with (1-sinA)]=[cosA(1-sinA)]/(1-sin²A)=(cosA-cosAsinA)/cos²A=[(cosA-cosAsinA)/sinA]/(cos²A/sinA)[dividing the numerator and the denominator by sinA]=[(cosA/sinA)-(cosAsinA/sinA)]/(cosA/sinA)cosA=(cotA-cosA)/cotAcosA (Proved) ? what sonam gandhi has done is that she solved out this sum by taking out the formul of cot a and cos a. And then she had proceeded the sum line by line or you can say that step by step |
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