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Relationship between Trigonometric Ratios

In ABC if ...

Question

In $△ A B C$ if $∠ B = 90^{o}$ then find $sin (A + C)$ .

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Solution

Given in $△ A B C$ if $∠ B = 90^{o}$ .
Then $A + C = 90^{o}$ . [ Since $A + B + C = 180^{o}$ ]
Then $sin (A + C) = sin 90^{o} = 1$ .

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△ A B C

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cos (A + C) = cos A cos C - sin A sin C

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△ A B C

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