Find the value of

, if sin A = and cos B=

Given

We know that,

Or

Let,

Side opposite to angle A = k

and Hypotenuse = k√2

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

⇒ (P)² + (B)² = (H)²

⇒ (k)² + (B)² = (k√2)²

⇒ k² + (B)² = 2k²

⇒ (B)² = 2k² – k²

⇒ (B)² = k²

⇒ B =√k²

⇒ B =±k [taking positive square root since, side cannot be negative]

So, Base = k

Now, we have to find the value of tan A

We know that,

So,

Now, we have to find the tan B

We know that,

Let,

Side adjacent to angle B =k√3

Hypotenuse =2k

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

⇒ (B)² + (P)² = (H)²

⇒ (k√3)² + (P)² = (2k)²

⇒ 3k² + (P)² = 4k²

⇒ (P)² = 4k² –3 k²

⇒ (P)² = k²

⇒ P =√k²

⇒ P =±k [taking positive square root since, side cannot be negative]

So, Perpendicular = k

Now, we have to find the value of sin B

We know that,

So,

Now,

Now, multiply and divide by the conjugate of √3 – 1, we get

[∵ (a – b)(a+b) = (a² – b²)]

⇒ 2+√3