Question

In ΔABC right angled at B, if tan A= √3, then cos A cos C- sin A sin C =

Answer 1

Answer:

final answer is zero.

Hope it helps

Answer 2

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In △ABC,

∠B=90⁰, tan A = ${\frac{1}{√3}}$ ${\implies}$ ${\frac{BC}{AB}}$

Let BC =1x,AB= √3

AC² = AB² + BC²

AC² = (√3x)² + (x)² = 4x²

AC = 2x

(i) sin A cos C + cos A sin C = ${\frac{1}{2}}$ × ${\frac{1}{2}}$ + ${\frac{√3}{2}}$ × ${\frac{√3}{2}}$ = ${\frac{1}{4}}$ ${\frac{3}{4}}$ = 1

(ii) cos A cos C - sin A sin C = ${\frac{√3}{2}}$ × ${\frac{1}{2}}$ - ${\frac{1}{2}}$ × ${\frac{√3}{2}}$ = ${\frac{√3}{4}}$ - ${\frac{√3}{4}}$ = 0

$\pmb{\mathbb{\fbox{\red{Hope it's help you}}}}$