Q. 42 D

# 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

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