Hướng dẫn giải Bài 6 (Trang 29 SGK Toán Đại số & Giải tích 11)

6. Với những giá trị nào của x thì giá trị của các hàm số y = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac><mo>-</mo><mi>x</mi></mrow></mfenced></math> và y=tan2x bằng nhau? Giải: Điều kiện <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>-</mo><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac><mo>≠</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mo>+</mo><mi>k</mi><mi mathvariant="normal">π</mi></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo> </mo><mo>≠</mo><mo> </mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mo>+</mo><mi>l</mi><mi mathvariant="normal">π</mi></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>≠</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">π</mi></mrow><mn>4</mn></mfrac><mo>+</mo><mi>k</mi><mi mathvariant="normal">π</mi></mtd></mtr><mtr><mtd><mi>x</mi><mo>≠</mo><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac><mo>+</mo><mi>l</mi><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced><mo>⇔</mo><mi>x</mi><mo>≠</mo><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac><mo>+</mo><mi>l</mi><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mo>(</mo><mi>l</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi><mo>)</mo></math> Ta có tan<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mi>tan</mi><mn>2</mn><mi>x</mi><mo>⇔</mo><mn>2</mn><mi>x</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac><mo>-</mo><mi>x</mi><mo> </mo><mo>+</mo><mi>k</mi><mi mathvariant="normal">π</mi><mo>⇔</mo><mi mathvariant="normal">x</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>12</mn></mfrac><mo>+</mo><mi mathvariant="normal">k</mi><mfrac><mi mathvariant="normal">π</mi><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mi mathvariant="normal">k</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi></math>