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