Question

IF √3 tanΘ = 3 sinΘ , find the value of sin²Θ - Cos²Θ.​

Answer 1

Answer:

Required value of sin^2 A - cos^2 A is 1 / 3.

Step-by-step explanation:

Given,

√3 tanA = 3 sinA

= > √3 tanA = 3 sinA

= > √3 = 3 sinA / tanA

= > √3 = 3 sinA x cosA / sinA

= > √3 = 3 cosA

= > 3 = 9 cos^2 A { square on both sides }

= > 3 / 9 = cos^2 A

= > 1 / 3 = cos^2 A

= > 2 / 3 = 2 cos^2 A

= > - 2 / 3 = - 2 cos^2 A

= > 1 - 2 / 3 = 1 - 2 cos^2 A

= > ( 3 - 2 ) / 3 = 1 - cos^2 A - cos^2 A

= > 1 / 3 = sin^2 A - cos^2 A { 1 - cos^2 B = sin^2 B }

Hence the required value of sin^2 A - cos^2 A is 1 / 3.

Answer 2

Answer:

√3 tanO = 3 SinO

TanO = √3 SinO

squaring

tan^2O = 3 sin^2O

sin^2O/cos^2O = 3 sin^2O

cos^2O = 1/3

sin^2O = 1-1/3 = 2/3

sin^2O - cos^2O

= 2/3-1/3

= 1/3