Question

In a ∆ABC right angled at B, ∠A = ∠C. Find the values of

(i) sin A cos C + cos A sin C
(ii) sin A sin B + cos A cos B

Answer 1

(i) We have drawn the following figure related to given information

To find:

…… (1)

Now we have,

,

,

Now by substituting the above values in equation (1)

We get,

Therefore,

…… (2)

Now in right angled

By applying Pythagoras theorem

We get,

Now, by substituting above value of AC² in equation (2)

We get,

Now both numerator and denominator contains

Therefore it gets cancelled and 1 remains

Hence

(ii) We have drawn the following figure

e

To find:

…… (1)

Now we know that sum of all the angles of any triangle is 180°

Therefore,

Since and

Therefore,

It is given that

Therefore,

…… (2)

Now we have,

,

,

Now by substituting the above values in equation (1)

We get,

Since

Therefore