This is an important question from
Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
This question has been asked in previous year exam
If tan A = 1/root3, find all other trigonometric ratios of angle A.
Please provide solution with figure
ML Aggarwal book, ICSE board, ques no. 4th
Solution:
Given, tan A = 1/√3
In right ∆ ABC,
tan A = BC/AB = 1/√3
So,
BC = 1 and AB = √3
By Pythagoras theorem,
AC = √(AB²+ BC²) = √[(√3)² + (1)²]
= √(3 + 1) = √4 = 2
Hence,
sin A = BC/AC = ½
cos A = AB/AC = √3/2
cot A = 1/tan A = √3
sec A = 1/cos A = 2/√3
cosec A = 1/sin A = 2/1 = 2