Question

In triangle ABC, right angle at B if cosec A = 2 , find value of
1/tanA + sinA/1+cosA​

Answer 1

Answer:

[Do not consider theta=30° in figure, it is mistake]

Step-by-step explanation:

Given: cosec A=2.

Cosec A=1/sin A=AC/BC=2/1

AC=2, BC=1

By Pythagoras theorem:

AC²=AB²+BC2

=>2²-1²=AB²

=>4-1=AB²

=>√3=AB.

tanA=BC/AB=1/√3

sinA=BC/AC=1/2.

cosA=AB/AC=√3/2

1/tanA+sinA/1+cosA

$= \frac{1}{ \frac{1}{ \sqrt{3} } } + \frac{1}{ \frac{2}{1 + \frac{ \sqrt{3} }{2} } }$

$= \frac{1}{ \frac{1}{ \sqrt{3} } } + \frac{1}{ \frac{2}{ \frac{2 + \sqrt{3} }{2} } }$

=√3+2+√3

=2√3+2.

Hope helps u.