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Trigonometric Ratios of Allied Angles

If A , B are ...

Question

If $A, B$ are supplementary angles, then the value of $sin A sin B - cos A cos B$ is

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Solution

Given $A + B = 180 °$
Now
$sin A sin B - cos A cos B = sin A sin (180 ° - A) - cos A cos (180 ° - A) = sin A sin A - cos A (- cos A) = {sin}^{2} A + {cos}^{2} A = 1$

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