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30. If COS A = m and COSA = n, then prove that(m2 + n2) cos²B = n2 |
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Answer» Given:cosA/cos B=m; cos A/sin B=n To prove:(m²+n²)cos²B=n²now (m²+n²)cos²B={(cos²A/cos² B)+(cos ²A/sin ²B}cos²B=cos²A{ (1/cos²B) + (1/sin ²B) }cos²B=cos ²A{(sin²B+cos ²B)/(sin²Bcos²B)cos²B =(cos ²A cos ²B)/(sin²Bcos²B)=(cos²A/sin²B)=n²=RHS |
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