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

1.	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» In a ∆ABC right angled at B, ∠A = ∠C, therefore ∠A = ∠C = 45° (i) sin A cos C + cos A sin C = sin (45° + 45°) = sin 90° = 1 (ii) sin A sin B + cos A cos B = cos (A + B) = cos (90° + 45°) = sin (45°) = \(\frac{1}{\sqrt{2}}\)

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»

In a ∆ABC right angled at B, ∠A = ∠C, therefore

∠A = ∠C = 45°

(i)

sin A cos C + cos A sin C

= sin (45° + 45°)

= sin 90°

= 1

(ii)

sin A sin B + cos A cos B

= cos (A + B)

= cos (90° + 45°)

= sin (45°)

= \(\frac{1}{\sqrt{2}}\)