Question

sin²A+cos²B =1 , A=30 find B​

Answer 1

Answer:

• The value of B = 30°

Step-by-step explanation:

Given that:

• sin²A + cos²B = 1
• The value of A = 30°

To Find:

• The value of B.

Substituting the value of A:

⇒ sin²30° + cos²B = 1

⇒ (1/2)² + cos²B = 1

⇒ 1/4 + cos²B = 1

⇒ cos²B = 1 - 1/4

⇒ cos²B = 4/4 - 1/4

⇒ cos²B = 3/4

⇒ cos B = √(3/4)

⇒ cos B = √3/2

• [∵ cos 30° = √3/2]

⇒ cos B = cos 30°

⇒ B = 30°

Trigonometric ratio:

• sin 0° = 0
• sin 30° = 1/2
• sin 45° = 1/√2
• sin 60° = √3/2
• sin 90° = 1

• cos 0° = 1
• cos 30° = √3/2
• cos 45° = 1/√2
• cos 60° = 1/2
• cos 90° = 0

• tan 0° = 0
• tan 30° = 1/√3
• tan 45° = 1
• tan 60° = √3
• tan 90° = undefined

Answer 2

Answer:

B = 30°

Step-by-step explanation:

Question:

$\sf{sin^2A+cos^2B =1 , \:A=30\: find \:B}$

Answer:

As angle a is 30°,

SinA can be written as Sin30°

$\sf{sin^2A+cos^2B =1}$

Substituting A= 30:

$\sf\dfrac{1}{2}^2$ + Cos²B = 1

$\sf\dfrac{1}{4}$ + Cos²B = 1

Cos²B = 1 - $\sf\dfrac{1}{4}$

Cos²B = $\sf\dfrac{3}{4}$

Take square root:

CosB = $\sf\dfrac{\sqrt3}{2}$

We know that:

Cos30° = $\sf\dfrac{\sqrt3}{2}$

Therefore,

CosB = Cos30°

B = 30°

Know more:

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$