Question

If 2 sinA : cos A = 5:6 , Then find the value of cot A, cos A and sin A.

Answer 1

2sinA:cosA=5:6
or, 2sinA/cosA=5/6
or, sinA/cosA=5/12
i.e., tanA=5/12
∴, cotA=1/tanA=12/5
tanA=5/12=perpendicular/base
By Pythagoras's theorem, perpendicular²+base²=hypotenuse²
∴, hypotenuse=√5²+12²=√25+144=√169=13
∴, sinA=perpendicular/hypotenuse=5/13 and
cosA=base/hypotenuse=12/13