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General Solution of Trigonometric Equation

If A+B=90,s...

Question

If $A + B = 90, sin A = a, sin B = b$ then $a^{2} + b^{2} = ?$

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Solution

The correct option is A $1$
Given $A + B = 90 ⟹ B = 90 - A$
And also given that $a = sin A, b = sin B = sin (90 - A) = cos A$
$a^{2} + b^{2} = {sin}^{2} A + {cos}^{2} A = 1$

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