Question

In right angled triangle ΔABC at B, ∠A = ∠C. Find the values of sin A sin B + cos A cos B

Answer 1

In Δle ABC ∠A + ∠B + ∠C = 180°

∠A + 90° + ∠A = 180°

2∠A = 90°

∠A = 45°

∴ ∠A = 45°  ....(1)

Adding ∠A = 45° (1) in sin A sin B + cos A cos B

∠A = 45° sin 90^@ + cos 45^@ cos 90^@

`1/sqrt2 . 1 + 0`

`= 1/sqrt2 . 1 + 0`

`= 1/sqrt2`