Question

If cos^2A/cot^2A-cos^2A=3, then find the value of 'A'​

Answer 1

Answer:

pls mark it as brainlest answer

Answer 2

Answer:

A = 60°

Step-by-step explanation:

Given:

$\dfrac{ { \cos }^{2} A}{\cot {}^{2} A - \cos {}^{2}A } = 3$

To find:

The value of A

Solution:

Just Simplify with Cross Multiple and Trigonometry Rule

$\dfrac{\cos^{2}A}{\cot^{2}A-\cos^{2}A}=3 \: \: \: \text{[Cross\:Multiple]}\\\\\cos^{2}A=3(\cot^{2}A-\cos^{2}A)\\\\\cos^{2}A=3\cot^{2}A-3\cos^{2}A\\\\\cos^{2}A+3\cos^{2}A=3\cot^{2}A\\\\4\cos^{2}A=3\cot^{2}A\\\\\cos^{2}A\times\frac{1}{\cot^{2}A}=\frac{3}{4}\\\\\sin^{2}A\:\times\:\frac{sin^{2}A}{cos^{2}A}=\frac{3}{4}\\\\sin\:A=\:\frac{\sqrt{3}}{2}\:\:\:[\:As\:\sin\:60^{\circ}\:=\:\frac{\sqrt{3}}{2}\:]\\\\\sin\:A\:=\:\sin\:60^{\circ}\\\\A\:=\:60$

Hence, The required value of A is 60°.

Important Trigonometry Rule

sin A = 1/cosec A

cos A = 1/sec A

tan A = 1/cot A = sin A/cos A