Question

If r sin a - tan a = 2/√3 and r cos a =2/3 then show that a= 60°, r=4/3

Answer 1

Answer:

. In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

R D Sharma Solutions For Class 10 Maths Chapter 5 Trigonometric Ratios ex 5.1 - 1

(i) sin A = 2/3

Solution:

We have,

sin A = 2/3 ……..….. (1)

As we know, by sin definition;

sin A = Perpendicular/ Hypotenuse = 2/3 ….(2)

By comparing eq. (1) and (2), we have

Opposite side = 2 and Hypotenuse = 3

Now, on using Pythagoras theorem in Δ ABC

AC2 = AB2 + BC2

Putting the values of perpendicular side (BC) and hypotenuse (AC) and for the base side as (AB), we get

⇒ 32 = AB2 + 22

AB2 = 32 – 22

AB2 = 9 – 4

AB2 = 5

AB = √5

Hence, Base = √5

By definition,

cos A = Base/Hypotenuse

⇒ cos A = √5/3

Since, cosec A = 1/sin A = Hypotenuse/Perpendicular

⇒ cosec A = 3/2

And, sec A = Hypotenuse/Base

⇒ sec A = 3/√5

And, tan A = Perpendicular/Base

⇒ tan A = 2/√5

And, cot A = 1/ tan A = Base/Perpendicular

⇒ cot A = √5/2