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In Right Angled Triangle δAbc at B, ∠A = ∠C. Find the Values of Sin a Sin B + Cos a Cos B - CBSE Class 10 - Mathematics

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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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Solution In Right Angled Triangle δAbc at B, ∠A = ∠C. Find the Values of Sin a Sin B + Cos a Cos B Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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