Question

this is a trigometrical ratio chapter please please please do this sum and send me now I am requesting to you all​

Answer 1

Step-by-step explanation:

Question:-

 If 3θ is an acute angle, solve the following equation for θ:

(cosec 3θ - 2)(cot 2θ - 1) = 0

Given:-

• (cosec 3θ - 2)(cot 2θ - 1) = 0

To Find:-

• The value of θ.

Formulas used:-

• cosec 30° = 2

• cosec 30° = 2cot 45° = 1

Solution:-

$\sf \implies (cosec 3 \theta - 2)(cot 2 \theta - 1) = 0$

$\sf \underline{cosec 3 \theta - 2 = 0 \: \: \: \: (or) \: \: \: cot 2 \theta - 1= 0}$

$\sf \implies cosec 3 \theta - 2 = 0$

$\sf \implies cosec 3 \theta = 2$

$\sf \implies cosec 3 \theta = cosec 30 ^{ \circ}$

$\sf \implies 3 \theta =30 ^{ \circ}$

$\sf \implies \theta = \dfrac{30 ^{ \circ}}{3}$

$\sf \dashrightarrow \boxed{\sf\theta = 10^{ \circ}}$

$\sf Now, \: \: cot 2 \theta - 1= 0$

$\sf \implies cot 2 \theta= 1$

$\sf \implies cot 2 \theta= cot45^{ \circ}$

$\sf \implies 2\theta= 45^{ \circ}$

$\sf \implies \theta= \dfrac{ 45^{ \circ}}{2}$

$\sf \dashrightarrow \boxed{\sf\theta = 22.5^{ \circ}}$

$\large\leadsto\underline{ \boxed{\sf \therefore \: \theta=10^{ \circ} \: \: (or) \: \: \: 22.5^{ \circ} }}$