if tan theta=3 sin theta, find the value of sin^2theta-cos^theta
URGENT!!
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Step-by-step explanation:
Given:-
Tan θ = 3 Sin θ
To find:-
Find the value of Sin^2 θ - Cos^2θ?
Solution:-
Given that
Tan θ = 3 Sin θ
=>Sin θ/ Cos θ = 3 Sin θ
=>On cancelling Sin θ both sides then
=>1/ Cos θ = 3
=>Cos θ = 1/3
On squaring both sides
=>Cos^2 θ = (1/3)^2
=>Cos^2 θ = 1/9----------(1)
=>1 - Cos^2 θ = 1-(1/9)
=>1- Cos^2 θ = (9-1)/9
=>1 - Cos^2 θ = 8/9
We know that
Sin^2 A + Cos^2 A=1
=>Sin^2 θ = 8/9-----------(2)
Now ,
Sin^2 θ - Cos^2 θ
From (1)&(2)
=>(8/9)-(1/9)
=>(8-1)/9
=>7/9
Answer:-
The value of Sin^2 θ - Cos^2 θ for the given problem is 7/9
Used formulae:-
- Sin^2 A + Cos^2 A=1
- Tan A = Sin A/ Cos A
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