Question

If sinθ= ⅗ evaluate cosθ . cot θ

Answer 1

Fig. is in the attachment....


We have,

Given:

Sin θ= ⅗ = perpendicular/ hypotenuse


We draw a right angle triangle at B such that perpendicular( BC) = 3  & hypotenuse AC = 5


By Pythagoras Theorem

AC² = AB²+ BC²

5²= AB² + 3²

25 = AB² + 9

25- 9 = AB²

16 = AB²

AB= √16 = 4

AB= 4


Base = 4



Cos θ = base / hypotenuse= AB/AC = 4/5


Cot θ = base/ perpendicular = AB/BC= 4/3


We have to find the value of

Cos θ . cot θ


4/5 × 4/3  =  16/15


Cos θ . cot θ= 16/15

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Hope this will help you....

Answer 2

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