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Substitution

If a 2 + b...

Question

If $a^{2} + b^{2} = 1, m^{2} + n^{2} = 1,$ then which of the following is true for all values of $m, n, a,$ $b -$

| a m + b n | \leq 1

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| a m - b n | \geq 1

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| a m + b n | \geq 1

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| a m - b n | \leq 1

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Solution

The correct options are
A $| a m + b n | \leq 1$
D $| a m - b n | \leq 1$

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\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}

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