Question

Triangle ABC, If. SinA+CosA/CosB=√2 Show that AngleC=135°

Answer 1

Please find the attachment

Answer 2

Concept:

Trigonometry is the relation between the angles of the triangle.

We can use trigonometric functions to find the length of the sides of the triangle.

Trigonometric functions are sine function, cosine functions,  tangent function, co-tangent function, secant function and co-secant function.

Given:

We are given that:

Sin A+ Cos A /Cos B=√2

Find:

We need to show that angle ∠C=135°

Solution:

sin A + cos A / cos B =√2

1/√2 sin A + 1/√2 cos A=cos B

sin π/4 sin A+ cos π/4 cos A=cos B

cos(-A+ π/4)=cos B

π/4-A=B

A+B=π/4=45

Now, we know that the sum of angles is 180 degrees.

A+B+C=180

45+C=180

C=180-45

C=135°

Therefore, the value of angle ∠C is 135°.

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