NEET Physics Crash Course - Basic Mathematics - NEET Maths

Basic Mathematics for NEET Physics

Essential Trigonometric Values and Triangles Trigonometric values for standard angles are crucial for solving physics problems efficiently. Memorizing values for $0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, and $90^\circ$ is essential, as well as understanding the 3-4-5 right triangle for quick recall of $\sin 37^\circ$ and...

Which of the following identities is/are not correct?

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>cos</mi><mi>&#952;</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>sin</mi><mi>&#952;</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>cos</mi><mi>&#952;</mi></mrow><mrow><mn>1</mn><mo>&#8722;</mo><mi>sin</mi><mi>&#952;</mi></mrow></mfrac><mo>=</mo><mn>2</mn></math>

$\&\#8747;\frac{dx}{1+3{\text{sin}}^{2}x+8{\text{cos}}^{2}x}=$

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac><msup><mtext>tan</mtext><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>2</mn><mtext>tan</mtext><mi>x</mi></mrow><mn>3</mn></mfrac></mfenced><mo>+</mo><mi>c</mi></math>

Which of the following identities is/are not correct?

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>cos</mi><mi>&#952;</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>sin</mi><mi>&#952;</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>cos</mi><mi>&#952;</mi></mrow><mrow><mn>1</mn><mo>&#8722;</mo><mi>sin</mi><mi>&#952;</mi></mrow></mfrac><mo>=</mo><mn>2</mn></math>

$\&\#8747;\frac{dx}{1+3{\text{sin}}^{2}x+8{\text{cos}}^{2}x}=$

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac><msup><mtext>tan</mtext><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>2</mn><mtext>tan</mtext><mi>x</mi></mrow><mn>3</mn></mfrac></mfenced><mo>+</mo><mi>c</mi></math>

What is the definition of an angle in radians?

Radians are a unit of angle measurement, defined such that $\theta = \frac{L}{R}$, where $L$ is the arc length and $R$ is the radius of a circle.

What are the sine, cosine, and tangent values for $37^\circ$ and $53^\circ$ based on the 3-4-5 right triangle?

For the 3-4-5 right triangle: $\sin 37^\circ = \frac{3}{5}$, $\cos 37^\circ = \frac{4}{5}$, $\tan 37^\circ = \frac{3}{4}$. And $\sin 53^\circ = \frac{4}{5}$, $\cos 53^\circ = \frac{3}{5}$, $\tan 53^\circ = \frac{4}{3}$.