Question

If tan A = 3/4 then find the value of 1/cot A +1 / Sin A.
Help me
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Answer 1

Solution :-

It is given that,

tanA = 3/4

Let the sides of the triangle be 3k and 4k

We know that,

tan Φ = Perpendicular / Base

Subsitute the required values,

tan A = 3k / 4k

By using Pythagoras theorem, we get :-

H² = P² + B²

H² = ( 3k)² + (4k)²

H² = 9k + 16k

H² = 25k

H = √25k = 5k

Now,

Sin A = Perpendicular / hypotenuse

Sin A = 3K / 5k

Sin A = 3/5

and

CotA = Hypotenuse / Perpendicular

CotA = 5k/3k

Cot A = 5/3

Now,

According to the question, we get :-

1/CotA + 1/SinA

Subsitute the required values

1/5/3 + 1/3/5

3/5 + 5/3

= 15 + 15/15

= 30/15

= 2

Hence, 2 is your answer $.$