this is a trigometrical ratio chapter please please please do this sum and send me now I am requesting to you all
Share
this is a trigometrical ratio chapter please please please do this sum and send me now I am requesting to you all
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
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:-
To Find:-
Formulas used:-
Solution:-
[tex]\sf \implies (cosec 3 \theta - 2)(cot 2 \theta - 1) = 0[/tex]
[tex]\sf \underline{cosec 3 \theta - 2 = 0 \: \: \: \: (or) \: \: \: cot 2 \theta - 1= 0}[/tex]
[tex]\sf \implies cosec 3 \theta - 2 = 0 [/tex]
[tex]\sf \implies cosec 3 \theta = 2 [/tex]
[tex]\sf \implies cosec 3 \theta = cosec 30 ^{ \circ} [/tex]
[tex]\sf \implies 3 \theta =30 ^{ \circ} [/tex]
[tex]\sf \implies \theta = \dfrac{30 ^{ \circ}}{3} [/tex]
[tex]\sf \dashrightarrow \boxed{\sf\theta = 10^{ \circ}}[/tex]
[tex]\sf Now, \: \: cot 2 \theta - 1= 0 [/tex]
[tex]\sf \implies cot 2 \theta= 1 [/tex]
[tex]\sf \implies cot 2 \theta= cot45^{ \circ} [/tex]
[tex]\sf \implies 2\theta= 45^{ \circ} [/tex]
[tex]\sf \implies \theta= \dfrac{ 45^{ \circ}}{2} [/tex]
[tex]\sf \dashrightarrow \boxed{\sf\theta = 22.5^{ \circ}}[/tex]
[tex] \large\leadsto\underline{ \boxed{\sf \therefore \: \theta=10^{ \circ} \: \: (or) \: \: \: 22.5^{ \circ} }} [/tex]