If A, B, C are the angles of a triangle,then | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the expression: $\sum \frac{\cot A + \cot B}{	an A + 	an B}$.We know that $\cot A + \cot B = \frac{\cos A}{\sin A} + \frac{\cos B}{\sin B}

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Given the expression: $\sum \frac{\cot A + \cot B}{	an A + 	an B}$.We know that $\cot A + \cot B = \frac{\cos A}{\sin A} + \frac{\cos B}{\sin B} = \frac{\sin B \cos A + \cos B \sin A}{\sin A \sin B} = \frac{\sin(A+B)}{\sin A \sin B}$.Similarly,$	an A + 	an B = \frac{\sin A}{\cos A} + \frac{\sin B}{\cos B} = \frac{\sin A \cos B + \cos A \sin B}{\cos A \cos B} = \frac{\sin(A+B)}{\cos A \cos B}$.Substituting these into the expression:$\frac{\cot A + \cot B}{	an A + 	an B} = \frac{\sin(A+B)}{\sin A \sin B} 	imes \frac{\cos A \cos B}{\sin(A+B)} = \frac{\cos A \cos B}{\sin A \sin B} = \cot A \cot B$.Thus,the sum is $\sum \cot A \cot B = \cot A \cot B + \cot B \cot C + \cot C \cot A$.For any triangle where $A + B + C = \pi$,the identity $\cot A \cot B + \cot B \cot C + \cot C \cot A = 1$ holds true.Therefore,the final answer is $1$.

If $A, B, C$ are the angles of a triangle,then $\sum \frac{\cot A + \cot B}{\tan A + \tan B} = $

Similar Questions

If $x = a \sin \theta - b \cos \theta$ and $y = a \cos \theta + b \sin \theta$,then which of the following is true?

If $x \cos \theta - \sin \theta = 1$,then $x^2 - (1 + x^2) \sin \theta$ equals

Minimum value of $5 \sin^2 \theta + 4 \cos^2 \theta$ is

If $A > 0, B > 0$ and $A + B = \frac{\pi}{6}$,then the minimum value of $\tan A + \tan B$ is

If $A = \sin^8 \theta + \cos^{14} \theta$,then for all real values of $\theta$:

Vedclass Test Series

Exam Paper Generator

Online Exam Module