Question

if 2 sin²theta-cos²theta=2 then find the value of o​

Answer 1

Answer:

90°

Step-by-step explanation:

⇒ 2sin²θ - cos²θ = 2

             Using cos²θ = 1 - sin²θ

⇒ 2sin²θ - (1 - sin²θ) = 2

⇒ 2sin²θ - 1 + sin²θ = 2

⇒ 3sin²θ = 3

⇒ sin²θ = 3/3

⇒ sin²θ = 1

⇒ sinθ = ± 1

          sinθ can't be negative(0<θ<90°), so

⇒ sinθ = 1 = sin90°

⇒ θ = 90°

Answer 2

Answer:

$\sf\tt\large{\red {\underline {\underline{⚘\;Question:}}}}$

• If
• $2 {sin}^{2} theta - {cos}^{2}theta = 2$

• then find the value of theta.

$\sf\tt\large{\green {\underline {\underline{⚘\;Solution:}}}}$

• $2 {sin }^{2} theta - {cos }^{2} theta = 2$

• Here by using formula which is ,

${cos}^{2} theta = 1 - {sin}^{2} theta$

• Then from this we get the result.

• $2 {sin}^{2} theta - 1(1 - {sin}^{2} theta)$

From,

• This we get that,

• $3 {sin}^{2} theta - 1 + {sin}^{2} theta = 2$

• $= 3 {sin}^{2} theta = 3$

• ${sin}^{2} theta = \frac{3}{3} = 1$

• ${sin}^{2} theta=1$

• $sin \: theta = \frac{ + }{ - } 1$

Therefore ,

• It cant be negative so ,

• $sin \: theta = 1 = sin {90}^{0}$
• Theta=90degree.

Hope it helps u mate .

Thank you .