Question

If tan A=1 and sin B =1/root2,find the value of cos(A+B),if A and B are acute angles

Answer 1

Answer:tan a= 1=tan 45

A=45

sin b=1/root2=sin 45

B=45

Cos a+b=cos90 =0

Step-by-step explanation:

Answer 2

Answer:

The value of Cos (A+B) is 0.

Step-by-step explanation:

In the question, it is given that,

tan A = 1 and Sin B = 1/✓2

We know that, tan 45° = 1

So tan A = tan 45°

So we can say that, the value of A is 45°.

A = 45°.

Similarly, Sin B = 1/✓2

We know that, Sin 45° = 1/✓2

So, Sin B = Sin 45°

Then B is 45°.

Cos (A+B)

= Cos (45°+45°)

= Cos 90°

= 0

Or,

Another process,

Cos (A+B) = Cos A Cos B - Sin A Sin B

Cos (A+B) = Cos 45° Cos 45° - Sin 45° Sin 45°

Cos (A+B) = 1/✓2 ×1/✓2 - 1/✓2 ×1/✓2

=1/2-1/2

=0